Question

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.What two rigid transformations were performed on figure ABCD
𝐴
𝐵
𝐶
𝐷
to produce the congruent figure WXYZ
𝑊
𝑋
𝑌
𝑍
?

(1 point)
Responses

ABCD
𝐴
𝐵
𝐶
𝐷
was first rotated 90°
90
°
(counterclockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated 90 degrees (counterclockwise), then shifted 3 units to the left and 5 units up.

ABCD
𝐴
𝐵
𝐶
𝐷
was first shifted 3 units to the left and 5 units up, then rotated 90°
90
°
(counterclockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated 90 degrees (counterclockwise).

ABCD
𝐴
𝐵
𝐶
𝐷
was first rotated −270°
−
270
°
( 270°
270
°
clockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated negative 270 degrees (270 degrees clockwise), then shifted 3 units to the left and 5 units up.

ABCD
𝐴
𝐵

Answer 1

First rotate ABCD 90° clockwise about the origin ( (x,y) → (y,−x) ), then translate 5 units right and 3 units up (add (5,3)).

Check:
- A(−6,−3) → rotate → (−3,6) → translate → (2,9) = W
- B(−6,−5) → (−5,6) → + (5,3) = (0,9) = X
- C(−4,−6) → (−6,4) → + (5,3) = (−1,7) = Y
- D(−3,−2) → (−2,3) → + (5,3) = (3,6) = Z

So the two rigid transformations are: 90° clockwise rotation, then translation right 5 and up 3.