2016年AMC10竞赛第16题5分
某個三角形的頂點座標爲 $$A(0,2)$$、 $$B(-3,2)$$、$$C(-3,0)$$ ，將此三角形以$$x$$軸爲對稱軸作對稱得到三角形$$\triangle A^{}\prime B^{}\prime C^{}\prime $$ ．再將她以原點爲中心，逆時針方向旋轉90°．得到$$\triangle A^{\prime \prime }B^{\prime \prime }C^{\prime \prime }$$．試問下列哪一個敘述能將變換回原來的？  $$\text{A}$$选项．繞原點逆時針旋轉$$90^{}\circ $$  $$\text{B}$$选项．繞原點順時針旋轉$$90^{}\circ $$  $$\text{C}$$选项．關於$$x$$軸的對稱  $$\text{D}$$选项．關於直線$$y=x$$對稱  $$\rm E$$选项．關於$$y$$軸的對稱  A triangle with vertices $$A(0,2)$$, $$B(-3,2)$$, and $$C(-3,0)$$ is reflected about the $$x$$-axis, then the image $$\triangle A^{}\prime B^{}\prime C^{}\prime $$ is rotated counterclockwise about the origin by $$90^{}\circ $$ to produce $$\triangle A^{\prime \prime }B^{\prime \prime }C^{\prime \prime }$$. Which of the following transformations will return $$\triangle A^{\prime \prime }B^{\prime \prime }C^{\prime \prime }$$ to $$\triangle ABC$$?
Consider a point $$(x,y)$$. Reflecting it about the $$x$$-axis will map it to $$(x,-y)$$, and rotating it counterclockwise about the origin by $$90^{}\circ $$will map it to $$(y,x)$$. The operation that undoes this is a reflection about the $$y=x$$, so the answer is $$\rm D$$. 