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Marvin Gaye (song)
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"Marvin Gaye"
Single by Charlie Puth featuring Meghan Trainor
from the album Some Type of Love and Nine Track Mind
Released
February 10, 2015[1]
Format
CD
digital download
Recorded
2014
Length
3:10
Label
Atlantic
Songwriter(s)
Charlie Puth
Julie Frost
Jacob Luttrell
Nick Seeley
Producer(s)
Charlie Puth
Charlie Puth singles chronology
"Marvin Gaye"
(2015) "See You Again"
(2015)
"Marvin Gaye"
(2015) "See You Again"
(2015)
Meghan Trainor singles chronology
"Lips Are Movin"
(2014) Lips Are Movin2014 "Marvin Gaye"
(2015) Marvin Gaye2015 "Dear Future Husband"
(2015) Dear Future Husband2015
Music video
"Marvin Gaye" on YouTube
"Marvin Gaye" is the debut single recorded, produced, and co-written by American singer Charlie Puth. It was released on February 10, 2015 by Atlantic Records as a single from Puth's third EP, Some Type of Love as well as the lead single from his debut album, Nine Track Mind,[1] it features guest vocals by Meghan Trainor. Puth co-wrote the song with Julie Frost, Jacob Luttrell and Nick Seeley.
"Marvin Gaye" topped the charts in the United Kingdom, Ireland, France, and New Zealand; peaked within the top 5 in Australia; and reached the top 40 in Austria, Canada and the United States.
Contents
[hide]
1 Background and release
2 Commercial performance
3 Music video
4 Live performances
5 Remix
6 Track listing
7 Charts
7.1 Weekly charts
7.2 Year-end charts
8 Certifications
9 References
10 External links
Background and release[edit]
"Marvin Gaye"
An 18-second sample of the chorus, where the lyrics are "an effort to spark romance and get that special someone in the mood."[2]
Problems playing this file? See media help.
Puth began his music career on YouTube,[3] gaining attention after recording with Emily Luther a cover of Adele's "Someone Like You".[3] The two appeared on The Ellen DeGeneres Show and signed with Ellen's record label, eleveneleven.[3] After gaining further attention, Puth signed with Atlantic Records[4] in January 2015.[5] Puth and Meghan Trainor announced a duet,[5] and "Marvin Gaye" was released as Puth's debut single on February 10, 2015.[1]
Puth said during an interview with Billboard that he had come up with the drumbeat for "Marvin Gaye" while sitting at a cafe in Hollywood,[6] adding that he and Trainor "were at a party one night, and we were exchanging the new music, and she heard "Marvin Gaye" and asked, "Who else is singing on this? It should be a duet. Let me sing on it!" So I'm like ... OK, Meghan Trainor just asked me to sing on my song, absolutely! In one day, she knew the whole thing. We did it all in one take."[6]
"Marvin Gaye" is a reference to the soul singer with "the lyrics of the tune being an effort to spark romance and get that special someone in the mood, just as many Gaye slow jams have done for millions in the past."[2] The song is also Trainor's first release without writing credits.[2] The collaboration led to Puth's appearance as one of Trainor's dates in the music video for her single "Dear Future Husband".[2] The references of Marvin Gaye in the song were criticized by some critics as a form of Cultural Appropriation which caused some controversy surrounding the release of the single.[7][8]
Commercial performance[edit]
In Oceania, "Marvin Gaye" became a commercial hit, peaking at number one in New Zealand[9] and number four in Australia.[10] It was later certified Platinum by Recorded Music New Zealand (RMNZ) and 2× Platinum by the Australian Recording Industry Association (ARIA).
In the United States, the song debuted at number 87 on the Billboard Hot 100[11] before peaking at number 21, making it Puth's second consecutive top 40 hit in the United States.
In the United Kingdom, the song debuted at number 90 on the UK Singles Chart before ascending to the top of the chart the following week, becoming both Puth and Trainor's second chart-topping single in Britain after "See You Again" and "All About That Bass" respectively.
In the Republic of Ireland, "Marvin Gaye" debuted at number 97 on the Irish Singles Chart before peaking at number-one five weeks later.[12]
Music video[edit]
The song's accompanying music video was directed by Marc Klasfeld[13] and released via YouTube on April 1, 2015.[14] It follows a dance in school where all in attendance "start making out on the floor, including the chaperones".[15] The video closes with Puth and Trainor kissing.[16]
The video featured a strong product placement for Fiat's then new 500 1957 Edition and was used prominently in the company's advertising.[17][18]
Live performances[edit]
Puth and Trainor performed "Marvin Gaye" during the 2015 American Music Awards on November 22, 2015. Like the music video, the performance ended with a kiss between the two. This led to speculation that the two were in a romantic relationship. Puth denied this, stating that he and Trainor are just "friends" and the kiss was only meant to keep the performance within the theme of the song. He further said, "There was a lot of making out. The dancers were making out and I'm sure some of the other dancers were making out. I think that's it though".[19]
Remix[edit]
An alternate version of "Marvin Gaye" has been released replacing Meghan Trainor with rapper Wale.[20] The remix is featured on the Japanese edition of Puth's album Nine Track Mind.[21]
Track listing[edit]
Digital download
No.
Title
Length
1. "Marvin Gaye" (featuring Meghan Trainor) 3:10
Charts[edit]
Weekly charts[edit]
Chart (2015–16)
Peak
position
Australia (ARIA)[10]
4
Austria (Ö3 Austria Top 40)[22]
3
Belgium (Ultratop 50 Flanders)[23]
12
Belgium (Ultratop 50 Wallonia)[24]
4
Canada (Canadian Hot 100)[25]
31
Czech Republic (Rádio Top 100)[26]
11
Czech Republic (Singles Digitál Top 100)[27]
21
Denmark (Tracklisten)[28]
28
Europe (Euro Digital Songs)[29]
1
Finland (Suomen virallinen lista)[30]
16
France (SNEP)[31]
1
Germany (Official German Charts)[32]
15
Hungary (Single Top 40)[33]
21
Iceland (RÚV)[34]
9
Ireland (IRMA)[12]
1
Israel (Media Forest)[35]
1
Italy (FIMI)[36]
6
Japan (Japan Hot 100)[37]
60
Luxembourg Digital Songs (Billboard)[38]
6
Mexico Ingles Airplay (Billboard)[39]
32
Netherlands (Dutch Top 40)[40]
11
Netherlands (Single Top 100)[41]
19
New Zealand (Recorded Music NZ)[9]
1
Norway (VG-lista)[42]
17
Poland (Polish Airplay Top 100) [43]
3
Scotland (Official Charts Company)[44]
1
Slovakia (Rádio Top 100)[45]
11
Slovakia (Singles Digitál Top 100)[46]
20
Slovenia (SloTop50)[47]
9
Spain (PROMUSICAE)[48]
3
Sweden (Sverigetopplistan)[49]
29
Switzerland (Schweizer Hitparade)[50]
2
UK Singles (Official Charts Company)[51]
1
US Billboard Hot 100[52]
21
US Adult Contemporary (Billboard)[53]
27
US Adult Top 40 (Billboard)[54]
12
US Mainstream Top 40 (Billboard)[55]
15
Year-end charts[edit]
Chart (2015)
Position
Australia (ARIA)[56]
38
Austria (Ö3 Austria Top 40)[57]
32
Belgium (Ultratop 50 Flanders)[58]
96
Belgium (Ultratop 50 Wallonia)[59]
99
Denmark (Tracklisten)[60]
87
Germany (Official German Charts)[61]
77
Israel (Media Forest)[62]
15
Italy (FIMI)[63]
38
New Zealand (Recorded Music NZ)[64]
17
Poland (ZPAV)[65]
16
Sweden (Sverigetopplistan)[66]
96
UK Singles (Official Charts Company)[67]
34
US Billboard Hot 100[68]
75
Chart (2016)
Position
Belgium (Ultratop 50 Wallonia)[69]
99
Slovenia (SloTop50)[70]
7
Switzerland (Schweizer Hitparade)[71]
96
Certifications[edit]
Region
Certification
Certified units/Sales
Australia (ARIA)[72]
2× Platinum 140,000^
Austria (IFPI Austria)[73]
Gold 15,000*
Belgium (BEA)[74]
Gold 15,000*
Canada (Music Canada)[75]
2× Platinum 160,000^
Denmark (IFPI Denmark)[76]
Platinum 60,000^
Germany (BVMI)[77]
Gold 200,000^
Italy (FIMI)[78]
3× Platinum 150,000
New Zealand (RMNZ)[79]
Platinum 15,000*
Norway (IFPI Norway)[80]
Platinum 10,000*
Spain (PROMUSICAE)[81]
Platinum 40,000^
Switzerland (IFPI Switzerland)[82]
Platinum 30,000^
United Kingdom (BPI)[83]
Platinum 600,000
United States (RIAA)[84]
2× Platinum 2,000,000
*sales figures based on certification alone
^shipments figures based on certification alone
sales+streaming figures based on certification alone
References[edit]
^ Jump up to: a b c "Marvin Gaye (feat. Meghan Trainor) – Single". iTunes Store (United States). Archived from the original on April 16, 2015. Retrieved April 17, 2015.
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^ Jump up to: a b c "Charlie Puth Has The Number One Song In The Country... So Who Is He?". Forbes. Retrieved April 25, 2015.
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External links[edit]
Lyrics of this song at MetroLyrics
[show]
v
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Charlie Puth
Discography
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Karl Mayer
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Karl Mayer
Portrayed by
Richard Burgi
Duration
2004–06, 2008, 2009–10, 2012
First appearance
"Pilot"
1x01, October 3, 2004
Last appearance
"Finishing the Hat"
8x23, May 13, 2012 (uncredited)
Created by
Marc Cherry
Profile
Occupation
Former
Lawyer
Strip club owner
[show]Family
Spouse
Susan Delfino (ex-wife; married twice)
Marissa Mayer (ex-wife)
Children
Julie Mayer (daughter, via Susan)
Evan Mayer (son, via Marissa)
Other relatives
Irene (Grandmother)[1]
Karl Mayer was a fictional character portrayed by Richard Burgi and created by television producer and screenwriter Marc Cherry for the ABC television series Desperate Housewives. He was the ex-husband of housewife Susan Mayer (Teri Hatcher) and father of Julie Mayer (Andrea Bowen), as well as a successful practitioner of family law. The character was also romantically involved in the series with two of other housewives: Edie Britt (Nicollette Sheridan) and Bree Van De Kamp (Marcia Cross). Karl died in Season 6, Episode 11 (If...) after injuries sustained when a plane crashed into Wisteria Lane during the Christmas Festival.
Contents
[hide]
1 Development and casting
2 History
2.1 Season 1
2.2 Season 2
2.3 Season 3
2.4 Season 4
2.5 Season 5
2.6 Season 6
2.7 Season 8
3 References
Development and casting[edit]
According to Cherry, casting the role of Karl was difficult because he "wanted a guy that was nice looking and seemed like he would have been married to Teri, but was also someone you wouldn't like."[2] The character was portrayed by another actor in a series of non-speaking flashbacks in the pilot episode, but the role was recast once the direction of the character changed.[2] After making some guest appearances during the first season, Burgi joined the regular cast in the second season. However, he returned to his guest starring status from the third season until his character's death halfway through the sixth season. Burgi returned for the series finale, appearing as his character's ghost among other deceased characters.
History[edit]
Season 1[edit]
Karl poses with his ex-wife Susan and his daughter Julie while having a picnic in a park.
Karl and Susan Mayer divorced a year prior to the events of the series as a result of Karl's affair with his secretary, Brandi.[3] In the season one episode "Move On", Karl ends his relationship with Brandi and asks Susan for a second chance, but she declines because of her commitment to Mike.[4] Susan also discovers that he flirted with Edie while they were married, and soon Karl starts dating Edie.
Season 2[edit]
Susan discovers that Karl is now living with Edie.[5] However, he is jealous of Mike Delfino and tries twice to get back with Susan.[6] He even goes so far as to lie to Susan and say that he was breaking it off with Edie, which led to him and Susan having sex. It is made obvious that Karl is still in love with Susan, as shown by several pictures of her that he secretly keeps around the house for him to look at from time to time.
Later Bree Van de Kamp hires Karl to stop her son, Andrew Van de Kamp from blackmailing her. Karl tells Andrew that even though Bree did witness George Williams die, she will not even face a courtroom. Andrew says that he will just make up stories or give her a "public humiliation" and Bree is horrified, Karl asks Bree for more tea and as Bree leaves for the kitchen, Karl grabs hold of Andrew and puts him against the wall and he says that he was a good friend to his father Rex Van de Kamp and said he knew if Rex was alive then he would force Andrew to behave. Andrew backchats once more but Karl grabs him by the cheek and says that if he doesn't stop blackmailing Bree and not giving her the respect she deserves then he will take care of Andrew himself. Bree overhears from the kitchen and lets out a sigh of relief.
Later in the season, Karl offers to marry Susan when she needs a life-saving surgery so that she can use his health insurance to pay for it, but they plan to divorce soon after Susan's surgery.[7] Karl becomes jealous of Susan and Dr. Ron McCready's relationship and he knows that Susan had not yet mentioned her and Mike's past, so Karl breaks open a pipe under the sink and Ron gets Mike and he learns that Susan had lied to him and Karl watched happily as Ron dumped her. Later in the series, Karl asks Edie to marry him; however, when Edie learns of their sham marriage, she demands that Karl propose to her and throw her a lavish wedding.[8] Karl and Susan sleep together one night and, as revenge, Edie burns Susan's house down, prompting Karl to buy her a new one as another attempt to get her back, only to be stopped by Mike. Karl eventually leaves Edie.[9]
Season 3[edit]
Karl appears only in the episode "Children and Art" to play the bad cop for Julie and Austin McCann. This backfires when he gets mad at Susan for dating Ian Hainsworth, a married English man whose wife is in a coma.
Season 4[edit]
Karl returns when Susan meets him at a Lamaze class as his pregnant new wife, Marissa (played by Sunny Mabrey), was there; Mike was not there as he was receiving his 30 days chip.[10] Karl constantly teases Susan about how things are going for him including Marissa being an author and a law student and him becoming partner of his firm and he constantly puts Mike down for referring to him as "the plumber". Susan however brings Mike along to the next class and makes herself and him dress up in order to impress Karl, where they both lie and say they have a party to go to after and that Mike now owns his company however Susan becomes disappointed when Mike mentions he was in rehab. When Susan confronts Karl, he tells her that Mike is a good guy and he'd be better for her then he ever would. In the five year leap on season five it's presumed Karl and Marissa had their child.
Season 5[edit]
Karl reappears in the second episode of the fifth season, where he was asked by Julie to pick up and help her with her insurance. He tells Susan he has been talking to her new love, painter Jackson Braddock, and teases her that she has now had a plumber and a painter and if he was a roofer they might still be together and Susan asks him to leave. Karl reappears yet again in the eighteenth episode of the fifth season, "A Spark. To Pierce the Dark.". Karl has enrolled his son Evan in Susan's art class, Susan gave the class an art assignment to draw what makes them happy and Evan drew his Mom being pierced with a sword. Susan felt concerned by this and called Karl to talk to him about his picture and Karl had confessed to Susan that Marissa had left them 6 weeks prior because she could not handle being a mother, and now Karl is caring for Evan by himself. Karl comments that he finally understands why it bothers Susan to see him and that he was truly sorry. Susan said that while she always wanted Karl to feel what he had done to her, it was not a great feeling and she was sorry that it happened to him.[11]
Bree later hires Karl as her divorce lawyer.[12] When Bree's husband, Orson Hodge, blackmails her into staying in the marriage, Karl and Bree begin an affair.
Season 6[edit]
Karl and Bree continue their affair during the first part of the sixth season. Karl decides to propose to Bree during the annual Christmas party, even hiring an engine plane with a banner behind it with the message "Will you marry me, Bree? Love, Karl" to fly over Wisteria Lane. Karl shows up in the party and tells Orson about the proposal and the two get into a fight in Santa's Workshop. Bree notices the activity going on inside Santa's Workshop, and goes in to stop Orson and Karl from fighting. When the plane slides into the party, it smashes into Santa's Workshop and after the crash a bloody hand is hanging out from one of the Workshop's windows.[13] It is revealed in the next episode that Karl died from his injuries from the crash. Part of the episode is devoted to Susan wondering what would have happened to her life if she had not divorced Karl, while another part centers on Bree contemplating a hypothetical marriage to Karl.[14] In his will, Karl leaves Susan his partial ownership of a local strip club.
Season 8[edit]
Richard Burgi makes one last, uncredited appearance as Karl in the series finale, "Finishing the Hat", as one of the ghosts that watch Susan and her family leave Wisteria Lane.
References[edit]
Jump up ^ Mentioned in season 6 episode 6
^ Jump up to: a b Touchstone Television, p. 85.
Jump up ^ "Pilot". Charles McDougall (director), Marc Cherry (writer). Desperate Housewives. ABC. October 3, 2004. Season 1, no. 1.
Jump up ^ "Move On". John David Coles (director), David Schulner (writer). Desperate Housewives. ABC. January 9, 2005. Season 1, no. 11.
Jump up ^ "You Could Drive a Person Crazy". David Grossman (director), Chris Black (writer), Alexandra Cunningham (writer). Desperate Housewives. ABC. October 2, 2005. Season 2, no. 2.
Jump up ^ "Could I Leave You?". Pam Thomas (director), Scott Sanford Tobis (writer). Desperate Housewives. ABC. March 26, 2006. Season 2, no. 17.
Jump up ^ "Silly People". Robert Duncan McNeill (director), Tom Spezialy (writer). Desperate Housewives. ABC. Season 2, no. 14.
Jump up ^ "Everybody Says Don't". Tom Cherones (director), Jenna Bans (writer), Alexandra Cunningham (writer). Desperate Housewives. ABC. April 2, 2006. Season 2, no. 18.
Jump up ^ "It Wasn't Meant to Happen". Larry Shaw (director), Marc Cherry (writer), Tom Spezialy (writer). Desperate Housewives. ABC. April 30, 2006. Season 2, no. 20.
Jump up ^ "Opening Doors". David Grossman (director), Dahvi Waller (writer), Jordon Nardino (writer). Desperate Housewives. ABC. May 4, 2008. Season 4, no. 14.
Jump up ^ "A Spark. To Pierce the Dark.". David Grossman (director), Alexandra Cunningham (writer). Desperate Housewives. ABC. March 22, 2009. Season 5, no. 18.
Jump up ^ "Bargaining". David Grossman (director), David Schladweiler (writer). Desperate Housewives. ABC. May 3, 2009. Season 5, no. 21.
Jump up ^ "Boom Crunch". David Grossman (director), John Pardee (writer), Joey Murphy (writer). Desperate Housewives. ABC. December 6, 2009. Season 6, no. 10.
Jump up ^ "If...". Larry Shaw (director), Jamie Gorenberg (writer). Desperate Housewives. ABC. January 3, 2010. Season 6, no. 11.
[show]
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Episodes
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Ex on the Beach (series 3)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Ex on the Beach
Series 3
Country of origin
United Kingdom
No. of episodes
10
Release
Original network
MTV
Original release
11 August – 13 October 2015
Season chronology
← Previous
Series 2
Next →
Series 4
The third series of Ex on the Beach, a British television programme, began airing on 11 August 2015 on MTV.[1] The series concluded on 13 October 2015 after 10 episodes. The group of cast members for this series included former The Only Way Is Essex star Kirk Norcross, whilst exes featured star of Geordie Shore and series 1 returnee Vicky Pattison as well as Rogan O'Connor who was an original cast member from the second series. Jordan Davies also joined the series as an ex having already appeared in Magaluf Weekender as well as Cami-Li, who appeared in fifteenth series of Celebrity Big Brother earlier in the year.[2] This was the first series where the "Tablet of Terror" gave the cast members the decision to evict one another in evil twists. As well as this, it was the first series to include a same-sex ex. The series was filmed in Cancún, Mexico.
Jordan Davies and Megan McKenna later returned during the fourth series entering as a couple.[3] Jordan made a third appearance during the fifth "All star" series, this time as main cast along with Bear and Jemma, and Holly returning as an ex again.[4] Shortly after this series, in 2016 it was announced that Marty McKenna had joined the cast of Geordie Shore for the twelfth series,[5] and was later joined by Sarah Goodhart for the fourteenth series.[6] Megan McKenna also went on to appear in the seventeenth series of Celebrity Big Brother[7] before later joining the cast of The Only Way Is Essex,[8] where as Stephen Bear also entered the house during the eighteenth series[9] and went on to win.[10] A year later in August 2017, both Jemma Lucy and Jordan Davies took part in the twentieth series.
Contents
[hide]
1 Cast
1.1 Duration of cast
1.1.1 Notes
2 Episodes
2.1 Ratings
3 References
4 External links
Cast[edit]
The official list of cast members were released on 14 July 2015. They include four boys; Graham Griffiths, Jayden Robins, Kirk Norcross, Stephen Bear, and four girls; Amy Cooke, Laura Summers and Megan McKenna, Megan Rees.[11] With the announcement of the line-up it was confirmed that former Geordie Shore cast member, and star of the first series Vicky Pattison would be making her return as an ex, alongside Series 2 star Rogan O'Connor. The Only Way Is Essex cast member Kirk Norcross was also confirmed to be taking part in the series, with his ex-fiancée and Celebrity Big Brother star Cami-Li featuring as his ex. The Magaluf Weekender star Jordan Davies was also revealed to be taking part in the series, also featuring as an ex.[12]
All original cast members arrived on the beach during the first episode where they were instantly told that they would soon be joined by their exes. Laura's ex-fling Jemma Lucy arrived at the villa during the first episode. This is the first time a same-sex ex has featured in the show. Also arriving in the first episode was Jordan Davies, an ex-boyfriend of Amy wanting to cause some trouble. Marty McKenna arrived during the next episode as the ex-romance of Jemma, then his ex-girlfriend Sarah Goodhart showed up during the third episode desperate to win back his affection. After much anticipation Cami-Li arrived at the beach during the fourth episode and instantly erupted at ex-fiancée Kirk. Soon after this, Kirk and Jemma's brief romance in the villa came to an end and they were added to each other's ex-list. The fifth episode featured the Tablet of Terrors new twist, which allowed Jordan to choose to send somebody home between Jayden and Megan M. He chose Jayden. As well as this, Jordan's ex-girlfriend Ali Drew made her first appearance at the beach, and Griff's ex Holly Rickwood arrived seeking his attention. Star of first series and Geordie Shore, Vicky Pattison arrived during the sixth episode as the ex-girlfriend of Kirk, but due to his ongoing arguments in the house, he voluntarily decided to leave the villa. Megan R's ex-boyfriend Stephen Cochrane made his debut during the seventh episode unsure of his intentions, and Marty was forced to leave the villa due to illness. The villa was left in shock during the eighth episode when the Tablet of Terror ordered Ali to send one of the exes home; she chose Vicky. Following this, Cami-Li decided to leave the beach having completed her mission to make Kirk's life a misery. Star of the second series, Rogan O'Connor also turned up on the beach as Jemma's ex. The ninth episode featured the arrival of Bear's ex-girlfriend and Megan M's ex-best friend Connie Wiltshire who intended to stir things up in the villa.
Bold indicates original cast member; all other cast were brought into the series as an ex.
Episodes
Name[13]
Age (at start of series)
Hometown
Exes
10 Amy Cooke 21 Cardiff Jordan Davies
10 Graham Griffiths 26 Wiltshire Holly Rickwood
5 Jayden Robins 30 London N/A
6 Kirk Norcross 26 Essex Cami-Li, Jemma Lucy, Vicky Pattison
10 Laura Summers 30 Manchester Jemma Lucy
10 Megan McKenna 22 Essex N/A
10 Megan Rees 20 Carmarthen Stephen Cochrane
10 Stephen Bear 25 East London Connie Wiltshire
10 Jemma Lucy 27 Manchester Kirk Norcross, Laura Summers, Marty McKenna, Rogan O'Connor
10 Jordan Davies 22 Cardiff Ali Drew, Amy Cooke
6 Marty McKenna 20 Newcastle Jemma Lucy, Sarah Goodhart
8 Sarah Goodhart 21 Newcastle Marty McKenna
5 Cami-Li 28 Miami Kirk Norcross
6 Ali Drew 25 Cardiff Jordan Davies
6 Holly Rickwood 23 Portsmouth Graham Griffiths
3 Vicky Pattison 26 Newcastle Kirk Norcross
4 Stephen Cochrane 25 Cornwall Megan Rees
3 Rogan O'Connor 25 Stratford-upon-Avon Jemma Lucy
2 Connie Wiltshire 20 Essex Stephen Bear
Duration of cast[edit]
Cast members
Episodes
1
2
3
4
5
6
7
8
9
10
Amy
Bear
Griff
Jayden
Kirk
Laura
Megan M
Megan R
Jemma
Jordan
Marty
Sarah
Cami-Li
Ali
Holly
Vicky
Stephen
Rogan
Connie
Notes[edit]
Key: = "Cast member" is featured in this episode.
Key: = "Cast member" arrives on the beach.
Key: = "Cast member" has an ex arrive on the beach.
Key: = "Cast member" arrives on the beach and has an ex arrive during the same episode.
Key: = "Cast member" leaves the beach.
Key: = "Cast member" has an ex arrive on the beach and leaves during the same episode.
Key: = "Cast member" does not feature in this episode.
Episodes[edit]
See also: List of Ex on the Beach episodes
No. in
series
No. in
season
Title
Original air date
Duration
UK viewers[14]
17
1 "Episode 1" 11 August 2015 (2015-08-11) 60 minutes 751,000
A brand new batch of singles arrive looking for love but are immediately regretting it after finding out their exes will be joining them. Bear and Megan M hit it off on their first date, but as he gets back to the villa it’s Amy who he’s smooching. Amy erupts when she hears that Bear has denied kissing her – but then ends up in his bed much to the annoyance of Megan M. As her attention draws to Kirk, Megan M is left instantly jealous when he takes a liking to Laura’s ex-flame Jemma instead. Following the first night drama, Amy feels isolated from the group, but things get a whole lot worse when her ex-boyfriend Jordan arrives at the beach.
18
2 "Episode 2" 18 August 2015 (2015-08-18) 60 minutes 861,000
Things get increasingly worse for Amy when she’s forced to listen to Megan R describe her date with Jordan, whilst Bear feels the wrath of Megan M when things get personal during a game of “Would you rather?”, causing Bear and Amy to find solace in each other’s arms. After making up the next day with Bear, Megan M rages with Amy when she discovers they’ve spent the night together and sets her sights on Jordan in an attempt to get back at her. Elsewhere Jemma and Kirk’s perfect date is interrupted by the arrival of her ex Marty, and Jayden and Griff clash.
19
3 "Episode 3" 25 August 2015 (2015-08-25) 60 minutes 719,000
The competition between Bear and Jordan intensifies as Megan M can’t decide who she likes more. After getting with Amy, Marty reports back to Jordan with harsh words about her, but they soon spread round the villa causing an almighty confrontation. Marty’s distraught following the arrival of his ex-girlfriend Sarah, who knows how to push his buttons when she goes on a date with Bear. Megan M finally makes up her mind and chooses to be with Jordan, whilst Bear returns to the villa to a warzone when the group discover that he’s been telling lies about them.
20
4 "Episode 4" 1 September 2015 (2015-09-01) 60 minutes 831,000
Bear wakes up to plenty of tension following the recent drama, but there’s more awkwardness as Marty goes on a date with all of his exes. Cami-Li arrives on the beach and immediately explodes with ex-fiancée Kirk. The villa erupts when Cami-Li gets personal with both Jemma and Laura, whilst Marty and Sarah end up having sex again. Kirk and Cami-Li finally settle their differences for the first time since their break-up, and he agrees not to get with Jemma again out of respect – but when he lies to Jemma about his promise, there are more kick-offs back at the villa.
21
5 "Episode 5" 8 September 2015 (2015-09-08) 60 minutes 821,000
Kirk isn’t happy with Jemma and Cami-Li’s new alliance. There’s trouble in paradise when Jordan’s ex-girlfriend arrives to stir things up between him and Megan M, and he plays right into her hands following a date together. Megan M releases her inner psycho once more with Ali on the receiving end, meanwhile Marty delivers some harsh home truths to Sarah after she suspects he’s getting close to Amy again. Elsewhere Jordan chooses to stay with Megan M, and Kirk and Griff end up in an almighty clash over Ali. Bear tries his luck with Griff’s ex Holly, and Kirk contemplates leaving.
22
6 "Episode 6" 15 September 2015 (2015-09-15) 60 minutes 769,000
Kirk and Ali get increasingly closer until Vicky’s arrival sparks trouble. Jemma and Cami-Li both predict that Kirk will return to his old habits and drop Ali for Vicky after spotting a connection. Megan M erupts once more with Ali accusing her of still having feelings for Jordan, whilst Bear leaves Holly devastated by ending their quick fling so he can concentrate on Vicky. After a hen night themed party, an emotional Kirk makes a move on Vicky but is left reeling after seeing her kissing Bear afterwards. Deciding he can’t cope in the villa anymore, Kirk packs his bags and leaves.
23
7 "Episode 7" 22 September 2015 (2015-09-22) 60 minutes 796,000
Holly struggles to believe Bear’s excuses as to why he doesn’t want to be with her anymore, whilst Megan M’s growing hatred towards Ali continues. A huge kick off in the villa reignites Megan R’s drama with Megan M. Laura takes a liking to new boy Stephen despite him being her best friend Megan R’s ex, so the pair’s instant connection causes a stir within the villa. Vicky decides to get closer with Bear believing he’s the one for her, whilst animosity is caused in the villa when Laura betrays her friend and attempts to get with Stephen despite promising not to make a move.
24
8 "Episode 8" 29 September 2015 (2015-09-29) 60 minutes 713,000
Cami-Li decides to leave the villa having accomplished her mission to ruin Kirk’s life, and Vicky’s temper is put to the test when Bear and Ali go on a date, but after hearing what the pair have been up to she’s left with no choice but to erupt. Ali is given the chance to send an ex home and chooses Vicky, whilst Megan R and Laura desperately try and compete for Stephen’s attention. Jemma’s ex Rogan arrives on the beach and instantly connects with Megan M causing jealousy for Jordan. Back at the villa the tensions reach boiling point when Megan M and Jordan clash, then goes up to the penthouse with Rogan as an act of revenge.
25
9 "Episode 9" 6 October 2015 (2015-10-06) 60 minutes 767,000
Deciding that getting with Megan M is too much drama, Rogan sets his sights on Ali instead. Megan R, Laura and Stephen are sent on an awkward date in the treetops where their issues don’t get resolved. Elsewhere Jordan rages after Megan M and Rogan kiss during a game of truth or dare, and he decides to play her at her own game. Stephen picks Laura but is left instantly regretting it, and Bear’s ex-girlfriend Connie arrives to reveal she used to be Megan M’s best friend before a betrayal, and there are fireworks when the pair eventually come face-to-face.
26
10 "Episode 10" 13 October 2015 (2015-10-13) 60 minutes 743,000
Megan M decides that she wants to win Jordan back but Griff is there to advise him against going back to her. As the group gather for the final banquet, Megan M and Connie finally put their differences aside, whilst a game of honesty explores some underlining issues. Laura is left red faced by Stephen, and Rogan is caught out winking at Megan M. With the tempers increasing, Rogan is put on the spot when Jordan demands an explanation for the wink, Griff stands up to Megan M, and Jordan confesses his feelings.
Ratings[edit]
Episode
Date
Official MTV rating[15]
MTV weekly rank[15]
Official MTV+1 rating[15]
Total MTV viewers
Episode 1
11 August 2015 728,000 1 23,000 751,000
Episode 2
18 August 2015 797,000 1 64,000 861,000
Episode 3
25 August 2015 690,000 1 29,000 719,000
Episode 4
1 September 2015 808,000 1 23,000 831,000
Episode 5
8 September 2015 768,000 1 53,000 821,000
Episode 6
15 September 2015 732,000 1 37,000 769,000
Episode 7
22 September 2015 749,000 1 47,000 796,000
Episode 8
29 September 2015 645,000 1 68,000 713,000
Episode 9
6 October 2015 726,000 1 41,000 767,000
Episode 10
13 October 2015 728,000 1 15,000 743,000
Average viewers
737,000 1 40,000 777,000
References[edit]
Jump up ^ "Ex On The Beach is back for its third series in August and it has celebrity exes galore". Digital Spy.
Jump up ^ "Ex On The Beach: Vicky returns alongside Kirk, Cami & Jordan Davies". Reveal.
Jump up ^ http://www.digitalspy.com/tv/ex-on-the-beach/news/a777226/meet-the-ex-on-the-beach-series-four-singles-including-geordie-shores-scotty-t/
Jump up ^ "Ex on the Beach cast tease the All-Star series". 4 July 2016.
Jump up ^ http://www.reveal.co.uk/showbiz-celeb-gossip/news/a677949/ex-on-the-beachs-marty-mckenna-joins-geordie-shore-for-season-12.html
Jump up ^ http://www.dailystar.co.uk/showbiz-tv/hot-tv/592258/Geordie-Shore-new-cast-series-14-Zahida-Allen-Sophie-Kasaei
Jump up ^ bbspy. "Official: Channel 5 confirms Celeb BB 2016 housemates". bbspy.co.uk.
Jump up ^ "Megan McKenna is joining The Only Way Is Essex". TellyMix.
Jump up ^ "Welcome to the madhouse! Webcam stripper Chloe Maffia, Geordie Shore's Marnie Simpson and American singer Aubrey O'Day make an eye-popping first impression in their skimpy ensembles as they lead the star-studded Celebrity Big Brother line-up". Daily Mail. 29 July 2016. Retrieved 29 July 2016.
Jump up ^ http://www.bbspy.co.uk/cbb18/news/0826/channel-5-reveals-celebrity-big-brother-summer-2016-final-voting-percentages-winner-bear-beat-ricky-by-just-1-percent-close-result
Jump up ^ "Ex On The Beach, Series 3: Kirk Norcross, Vicky Pattison plus all the other sexy singles!". heatworld.
Jump up ^ "Ex On The Beach: Vicky returns alongside Kirk, Cami & Jordan Davies". Reveal.
Jump up ^ "OMG! Check Out The Ex On The Beach 2 Hotties! - MTV UK". MTV UK.
Jump up ^ "Top 10 Programmes". BARB. Archived from the original on 18 July 2014. Retrieved 2013-07-12.
^ Jump up to: a b c "Top 10 Programmes". Broadcasters' Audience Research Board. Retrieved 30 April 2013.
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text:
Distance from a point to a line
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Knowing the shortest distance from a point to a line can be useful in various situations—for example, finding the shortest distance to reach a road, quantifying the scatter on a graph, etc. In Deming regression, a type of linear curve fitting, if the dependent and independent variables have equal variance this results in orthogonal regression in which the degree of imperfection of the fit is measured for each data point as the perpendicular distance of the point from the regression line.
Contents
1 Cartesian coordinates
1.1 Line defined by an equation
1.2 Line defined by two points
2 Proofs
2.1 An algebraic proof
2.2 A geometric proof
2.3 A vector projection proof
3 Another formula
4 Vector formulation
5 Another vector formulation
6 See also
7 Notes
8 References
9 Further reading
Cartesian coordinates[edit]
Line defined by an equation[edit]
In the case of a line in the plane given by the equation ax + by + c = 0, where a, b and c are real constants with a and b not both zero, the distance from the line to a point (x0,y0) is[1][2]:p.14
distance  ( a x + b y + c = 0 , ( x 0 , y 0 ) ) = | a x 0 + b y 0 + c | a 2 + b 2 . {\displaystyle \operatorname {distance} (ax+by+c=0,(x_{0},y_{0}))={\frac {|ax_{0}+by_{0}+c|}{\sqrt {a^{2}+b^{2}}}}.}
The point on this line which is closest to (x0,y0) has coordinates:[3]
x = b ( b x 0 − a y 0 ) − a c a 2 + b 2 and y = a ( − b x 0 + a y 0 ) − b c a 2 + b 2 . {\displaystyle x={\frac {b(bx_{0}-ay_{0})-ac}{a^{2}+b^{2}}}{\text{ and }}y={\frac {a(-bx_{0}+ay_{0})-bc}{a^{2}+b^{2}}}.}
Horizontal and vertical lines
In the general equation of a line, ax + by + c = 0, a and b cannot both be zero unless c is also zero, in which case the equation does not define a line. If a = 0 and b ≠ 0, the line is horizontal and has equation y = -c/b. The distance from (x0, y0) to this line is measured along a vertical line segment of length |y0 - (-c/b)| = |by0 + c| / |b| in accordance with the formula. Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax0 + c| / |a|, as measured along a horizontal line segment.
Line defined by two points[edit]
If the line passes through two points P1=(x1,y1) and P2=(x2,y2) then the distance of (x0,y0) from the line is:
distance  ( P 1 , P 2 , ( x 0 , y 0 ) ) = | ( y 2 − y 1 ) x 0 − ( x 2 − x 1 ) y 0 + x 2 y 1 − y 2 x 1 | ( y 2 − y 1 ) 2 + ( x 2 − x 1 ) 2 . {\displaystyle \operatorname {distance} (P_{1},P_{2},(x_{0},y_{0}))={\frac {|(y_{2}-y_{1})x_{0}-(x_{2}-x_{1})y_{0}+x_{2}y_{1}-y_{2}x_{1}|}{\sqrt {(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}}}.}
The denominator of this expression is the distance between P1 and P2. The numerator is twice the area of the triangle with its vertices at the three points, (x0,y0), P1 and P2. See: Area of a triangle § Using coordinates. The expression is equivalent to h = 2 A b {\textstyle h={\frac {2A}{b}}} , which can be obtained by rearranging the standard formula for the area of a triangle: A = 1 2 b h {\textstyle A={\frac {1}{2}}bh} , where b is the length of a side, and h is the perpendicular height from the opposite vertex.
Proofs[edit]
An algebraic proof[edit]
This proof is only valid if the line is neither vertical nor horizontal, that is, we assume that neither a nor b in the equation of the line is zero.
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x0, y0). The line through these two points is perpendicular to the original line, so
y 0 − n x 0 − m = b a . {\displaystyle {\frac {y_{0}-n}{x_{0}-m}}={\frac {b}{a}}.}
Thus, a ( y 0 − n ) − b ( x 0 − m ) = 0 , {\displaystyle a(y_{0}-n)-b(x_{0}-m)=0,} and by squaring this equation we obtain:
a 2 ( y 0 − n ) 2 + b 2 ( x 0 − m ) 2 = 2 a b ( y 0 − n ) ( x 0 − m ) . {\displaystyle a^{2}(y_{0}-n)^{2}+b^{2}(x_{0}-m)^{2}=2ab(y_{0}-n)(x_{0}-m).}
Now consider,
( a ( x 0 − m ) + b ( y 0 − n ) ) 2 = a 2 ( x 0 − m ) 2 + 2 a b ( y 0 − n ) ( x 0 − m ) + b 2 ( y 0 − n ) 2 = ( a 2 + b 2 ) ( ( x 0 − m ) 2 + ( y 0 − n ) 2 ) {\displaystyle (a(x_{0}-m)+b(y_{0}-n))^{2}=a^{2}(x_{0}-m)^{2}+2ab(y_{0}-n)(x_{0}-m)+b^{2}(y_{0}-n)^{2}=(a^{2}+b^{2})((x_{0}-m)^{2}+(y_{0}-n)^{2})}
using the above squared equation. But we also have,
( a ( x 0 − m ) + b ( y 0 − n ) ) 2 = ( a x 0 + b y 0 − a m − b n ) 2 = ( a x 0 + b y 0 + c ) 2 {\displaystyle (a(x_{0}-m)+b(y_{0}-n))^{2}=(ax_{0}+by_{0}-am-bn)^{2}=(ax_{0}+by_{0}+c)^{2}}
since (m, n) is on ax + by + c = 0. Thus,
( a 2 + b 2 ) ( ( x 0 − m ) 2 + ( y 0 − n ) 2 ) = ( a x 0 + b y 0 + c ) 2 {\displaystyle (a^{2}+b^{2})((x_{0}-m)^{2}+(y_{0}-n)^{2})=(ax_{0}+by_{0}+c)^{2}}
and we obtain the length of the line segment determined by these two points,
d = ( x 0 − m ) 2 + ( y 0 − n ) 2 = | a x 0 + b y 0 + c | a 2 + b 2 . {\displaystyle d={\sqrt {(x_{0}-m)^{2}+(y_{0}-n)^{2}}}={\frac {|ax_{0}+by_{0}+c|}{\sqrt {a^{2}+b^{2}}}}.} [4]
A geometric proof[edit]
Diagram for geometric proof
This proof is valid only if the line is not horizontal or vertical.[5]
Drop a perpendicular from the point P with coordinates (x0, y0) to the line with equation Ax + By + C = 0. Label the foot of the perpendicular R. Draw the vertical line through P and label its intersection with the given line S. At any point T on the line, draw a right triangle TVU whose sides are horizontal and vertical line segments with hypotenuse TU on the given line and horizontal side of length |B| (see diagram). The vertical side of ∆TVU will have length |A| since the line has slope -A/B.
∆PRS and ∆TVU are similar triangles, since they are both right triangles and ∠PSR ≅ ∠TUV since they are corresponding angles of a transversal to the parallel lines PS and UV (both are vertical lines).[6] Corresponding sides of these triangles are in the same ratio, so:
| P R ¯ | | P S ¯ | = | T V ¯ | | T U ¯ | . {\displaystyle {\frac {|{\overline {PR}}|}{|{\overline {PS}}|}}={\frac {|{\overline {TV}}|}{|{\overline {TU}}|}}.}
If point S has coordinates (x0,m) then |PS| = |y0 - m| and the distance from P to the line is:
| P R ¯ | = | y 0 − m | | B | A 2 + B 2 . {\displaystyle |{\overline {PR}}|={\frac {|y_{0}-m||B|}{\sqrt {A^{2}+B^{2}}}}.}
Since S is on the line, we can find the value of m,
m = − A x 0 − C B , {\displaystyle m={\frac {-Ax_{0}-C}{B}},}
and finally obtain:[7]
| P R ¯ | = | A x 0 + B y 0 + C | A 2 + B 2 . {\displaystyle |{\overline {PR}}|={\frac {|Ax_{0}+By_{0}+C|}{\sqrt {A^{2}+B^{2}}}}.}
A variation of this proof is to place V at P and compute the area of the triangle ∆UVT two ways to obtain that D | T U ¯ | = | V U ¯ | | V T ¯ | {\displaystyle D|{\overline {TU}}|=|{\overline {VU}}||{\overline {VT}}|} where D is the altitude of ∆UVT drawn to the hypoteneuse of ∆UVT from P. The distance formula can then used to express | T U ¯ | {\displaystyle |{\overline {TU}}|} , | V U ¯ | {\displaystyle |{\overline {VU}}|} , and | V T ¯ | {\displaystyle |{\overline {VT}}|} in terms of the coordinates of P and the coefficients of the equation of the line to get the indicated formula.[citation needed]
A vector projection proof[edit]
Let P be the point with coordinates (x0, y0) and let the given line have equation ax + by + c = 0. Also, let Q = (x1, y1) be any point on this line and n the vector (a, b) starting at point Q. The vector n is perpendicular to the line, and the distance d from point P to the line is equal to the length of the orthogonal projection of Q P → {\displaystyle {\overrightarrow {QP}}} on n. The length of this projection is given by:
d = | Q P → ⋅ n | ‖ n ‖ . {\displaystyle d={\frac {|{\overrightarrow {QP}}\cdot \mathbf {n} |}{\|\mathbf {n} \|}}.}
Now,
Q P → = ( x 0 − x 1 , y 0 − y 1 ) , {\displaystyle {\overrightarrow {QP}}=(x_{0}-x_{1},y_{0}-y_{1}),} so Q P → ⋅ n = a ( x 0 − x 1 ) + b ( y 0 − y 1 ) {\displaystyle {\overrightarrow {QP}}\cdot \mathbf {n} =a(x_{0}-x_{1})+b(y_{0}-y_{1})} and ‖ n ‖ = a 2 + b 2 , {\displaystyle \|\mathbf {n} \|={\sqrt {a^{2}+b^{2}}},}
thus
d = | a ( x 0 − x 1 ) + b ( y 0 − y 1 ) | a 2 + b 2 . {\displaystyle d={\frac {|a(x_{0}-x_{1})+b(y_{0}-y_{1})|}{\sqrt {a^{2}+b^{2}}}}.}
Since Q is a point on the line, c = − a x 1 − b y 1 {\displaystyle c=-ax_{1}-by_{1}} , and so,[8]
d = | a x 0 + b y 0 + c | a 2 + b 2 . {\displaystyle d={\frac {|ax_{0}+by_{0}+c|}{\sqrt {a^{2}+b^{2}}}}.}
Another formula[edit]
It is possible to produce another expression to find the shortest distance of a point to a line. This derivation also requires that the line is not vertical or horizontal.
The point P is given with coordinates ( x 0 , y 0 {\displaystyle x_{0},y_{0}} ). The equation of a line is given by y = m x + k {\displaystyle y=mx+k} . The equation of the normal of that line which passes through the point P is given y = x 0 − x m + y 0 {\displaystyle y={\frac {x_{0}-x}{m}}+y_{0}} .
The point at which these two lines intersect is the closest point on the original line to the point P. Hence:
m x + k = x 0 − x m + y 0 . {\displaystyle mx+k={\frac {x_{0}-x}{m}}+y_{0}.}
We can solve this equation for x,
x = x 0 + m y 0 − m k m 2 + 1 . {\displaystyle x={\frac {x_{0}+my_{0}-mk}{m^{2}+1}}.}
The y coordinate of the point of intersection can be found by substituting this value of x into the equation of the original line,
y = m ( x 0 + m y 0 − m k ) m 2 + 1 + k . {\displaystyle y=m{\frac {(x_{0}+my_{0}-mk)}{m^{2}+1}}+k.}
Using the equation for finding the distance between 2 points, d = ( X 2 − X 1 ) 2 + ( Y 2 − Y 1 ) 2 {\displaystyle d={\sqrt {(X_{2}-X_{1})^{2}+(Y_{2}-Y_{1})^{2}}}} , we can deduce that the formula to find the shortest distance between a line and a point is the following:
d = ( x 0 + m y 0 − m k m 2 + 1 − x 0 ) 2 + ( m x 0 + m y 0 − m k m 2 + 1 + k − y 0 ) 2 = | k + m x 0 − y 0 | 1 + m 2 . {\displaystyle d={\sqrt {\left({{\frac {x_{0}+my_{0}-mk}{m^{2}+1}}-x_{0}}\right)^{2}+\left({m{\frac {x_{0}+my_{0}-mk}{m^{2}+1}}+k-y_{0}}\right)^{2}}}={\frac {|k+mx_{0}-y_{0}|}{\sqrt {1+m^{2}}}}.}
Recalling that m = -a/b and k = - c/b for the line with equation ax + by + c = 0, a little algebraic simplification reduces this to the standard expression.[9]
Vector formulation[edit]
Illustration of the vector formulation.
The equation of a line can be given in vector form:
x = a + t n {\displaystyle \mathbf {x} =\mathbf {a} +t\mathbf {n} }
Here a is the position of a point on the line, and n is a unit vector in the direction of the line. Then as scalar t varies, x gives the locus of the line.
The distance of an arbitrary point p to this line is given by
distance  ( x = a + t n , p ) = ‖ ( a − p ) − ( ( a − p ) ⋅ n ) n ‖ . {\displaystyle \operatorname {distance} (\mathbf {x} =\mathbf {a} +t\mathbf {n} ,\mathbf {p} )=\|(\mathbf {a} -\mathbf {p} )-((\mathbf {a} -\mathbf {p} )\cdot \mathbf {n} )\mathbf {n} \|.}
This formula can be derived as follows: a − p {\displaystyle \mathbf {a} -\mathbf {p} } is a vector from p to the point a on the line. Then ( a − p ) ⋅ n {\displaystyle (\mathbf {a} -\mathbf {p} )\cdot \mathbf {n} } is the projected length onto the line and so
( ( a − p ) ⋅ n ) n {\displaystyle ((\mathbf {a} -\mathbf {p} )\cdot \mathbf {n} )\mathbf {n} }
is a vector that is the projection of a − p {\displaystyle \mathbf {a} -\mathbf {p} } onto the line. Thus
( a − p ) − ( ( a − p ) ⋅ n ) n {\displaystyle (\mathbf {a} -\mathbf {p} )-((\mathbf {a} -\mathbf {p} )\cdot \mathbf {n} )\mathbf {n} }
is the component of a − p {\displaystyle \mathbf {a} -\mathbf {p} } perpendicular to the line. The distance from the point to the line is then just the norm of that vector.[10] This more general formula is not restricted to two dimensions.
Another vector formulation[edit]
If the vector space is orthonormal and if the line (l ) goes through point A and has a direction vector u → {\displaystyle {\vec {u}}} , the distance between point P and line (l) is
d ( P , ( l ) ) = ‖ A P → × u → ‖ ‖ u → ‖ {\displaystyle d(\mathrm {P} ,(l))={\frac {\left\|{\overrightarrow {\mathrm {AP} }}\times {\vec {u}}\right\|}{\|{\vec {u}}\|}}}
where A P → × u → {\displaystyle {\overrightarrow {\mathrm {AP} }}\times {\vec {u}}} is the cross product of the vectors A P → {\displaystyle {\overrightarrow {\mathrm {AP} }}} and u → {\displaystyle {\vec {u}}} and where ‖ u → ‖ {\displaystyle \|{\vec {u}}\|} is the vector norm of u → {\displaystyle {\vec {u}}} .
Note that cross products only exist in dimensions 3 and 7.
See also[edit]
Hesse normal form
Line-line intersection
Distance between two lines
Distance from a point to a plane
Skew lines#Distance
Notes[edit]
Jump up ^ Larson & Hostetler 2007, p. 452
Jump up ^ Spain 2007
Jump up ^ Larson & Hostetler 2007, p. 522
Jump up ^ Between Certainty and Uncertainty: Statistics and Probability in Five Units With Notes on Historical Origins and Illustrative Numerical Examples
Jump up ^ Ballantine & Jerbert 1952 do not mention this restriction in their article
Jump up ^ If the two triangles are on opposite sides of the line, these angles are congruent because they are alternate interior angles.
Jump up ^ Ballantine & Jerbert 1952
Jump up ^ Anton 1994, pp. 138-9
Jump up ^ Larson & Hostetler 2007, p. 522
Jump up ^ Sunday, Dan. "Lines and Distance of a Point to a Line". softSurfer. Retrieved 6 December 2013.
References[edit]
Anton, Howard (1994), Elementary Linear Algebra (7th ed.), John Wiley & Sons, ISBN 0-471-58742-7
Ballantine, J.P.; Jerbert, A.R. (1952), "Distance from a line or plane to a point", American Mathematical Monthly, 59: 242–243, doi:10.2307/2306514
Larson, Ron; Hostetler, Robert (2007), Precalculus: A Concise Course, Houghton Mifflin Co., ISBN 0-618-62719-7
Spain, Barry (2007) [1957], Analytical Conics, Dover Publications, ISBN 0-486-45773-7
Further reading[edit]
Deza, Michel Marie; Deza, Elena (2013), Encyclopedia of Distances (2nd ed.), Springer, p. 86, ISBN 9783642309588
Retrieved from "https://en.wikipedia.org/w/index.php?title=Distance_from_a_point_to_a_line&oldid=837108058"
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