Now that we have the preimage, we can create the image using the translation (x,y) → (x+ 4,y- 2). This translation tells us that for every point in ABCD, we should add 4 to each x-coordinate and subtract 2 from each y-coordinate.
ccc
(x,y) &→ &(x+ 4,y- 2)
A(-4,1) &→ & A'(0,-1)
B(-3,3) &→ & B'(1,1)
C(0,1) &→ & C'(4,-1)
D(-2,0) &→ & D'(2,-2)
Now we have the points for the image. Let's add them to the same coordinate plane as the preimage.
We can see that the translation moved the points to the right and down. Finally, we can connect the points to have the new quadrilateral.
