Polygon ABCD has the vertices A(2, 8), B(4, 12), C(10, 12), and D(8, 8), and polygon MNOP has the vertices M(-2, 8), N(-4, 12), O(-10, 12), and P(-8, 8). Which transformation can you perform on polygon ABCD to show that polygons ABCD and MNOP are congruent?

Question

mathmate · Answer

Review the following simple transformations:
$S_x: (x,y)\rightarrow (x,-y)$  reflection about x axis
$S_y: (x,y)\rightarrow (-x,y)$  reflection about y axis
$S_{y=x}: (x,y)\rightarrow (y,x)$  reflection about y=x
$R_{90}: (x,y)\rightarrow (-y,x)$ rotation 90 degrees counter-clockwise
$R_{180}: (x,y)\rightarrow (-x,-y)$ rotation 180 degrees 
$R_{270}: (x,y)\rightarrow (-x,y)$  rotation 270 degrees counter-clockwise
$T_{(dx,dy)}: (x,y)\rightarrow (x+dx,y+dy)$ translation of (dx,dy)
Identify which of the transformations was performed.

recall that 
A$\rightarrow$M
B$\rightarrow$N
C$\rightarrow$O
D$\rightarrow$P