Question

Que

Point upper A has coordinates left parenthesis negative 6 comma negative 3 right parenthesis. Point upper B has coordinates left parenthesis negative 6 comma negative 5 right parenthesis. Point upper C has coordinates left parenthesis negative 4 comma negative 6 right parenthesis. Point upper D has coordinates left parenthesis negative 3 comma negative 2 right parenthesis. Point upper W has coordinates left parenthesis 2 comma 9 right parenthesis. Point upper X has coordinates left parenthesis 0 comma 9 right parenthesis. Point upper Y has coordinates left parenthesis negative 1 comma 7 right parenthesis. Point upper Z has coordinates left parenthesis 3 comma 6 right parenthesis.


Image Long DescriptionPoint upper A has coordinates left parenthesis negative 6 comma negative 3 right parenthesis. Point upper B has coordinates left parenthesis negative 6 comma negative 5 right parenthesis. Point upper C has coordinates left parenthesis negative 4 comma negative 6 right parenthesis. Point upper D has coordinates left parenthesis negative 3 comma negative 2 right parenthesis. Point upper W has coordinates left parenthesis 2 comma 9 right parenthesis. Point upper X has coordinates left parenthesis 0 comma 9 right parenthesis. Point upper Y has coordinates left parenthesis negative 1 comma 7 right parenthesis. Point upper Z has coordinates left parenthesis 3 comma 6 right parenthesis.

What two rigid transformations were performed on figure ABCD
to produce the congruent figure WXYZ
?

Answer 1

First rotate ABCD 90° clockwise about the origin (equivalently 270° counterclockwise). Then translate the result by the vector (5, 3) — i.e. 5 units right and 3 units up.

Check: rotating A(-6,-3) 90° clockwise gives (-3,6); adding (5,3) gives W(2,9). The same two steps send B→X, C→Y, D→Z.