:quadrilateral abcd is located at a(-2,2) b(-2,4) g(2,4) d(2,2). the quadrilateral is then transformed using the rule (x+2,y-3) to form the image a'b'c'd'. what are the new coordinates of of a'b'c'd'? describe what characteristics you would find if the corresponding vertices were connected with line segments.

The given rule is a translation to the right (2 steps) and down (3 steps).
In order to find the new coordinates, you need to take the given x and add 2 and the given y and subtract 3.
Therefore:
A' (-2+2 , 2-3) --> (0,-1)
B' (-2+2 , 4-3) --> (0,1)
C' (2+2 , 4-3) --> (4,1)
D' (2+2, 2-3) --> (4,-1)

Since the quadrilaterals ABCD and A'B'C'D' are rectangles, connecting the corresponding vertices would give you a parallelepiped, which means that AA', BB', CC', DD' are parallel and congruent segments. 

Did you get there answer to 44?