Question

Rectangle A'B'C'D' is the image of rectangle ABCD after it has been translated according to the rule T–4, 3(x, y).

On a coordinate plane, a rectangles has points A prime (negative 5, 4), B prime (3, 4), C prime (3, 1), and D prime (negative 5, 1).
Which points are vertices of the pre-image, rectangle ABCD? Select four options.

(–1, –2)
(7, 1)
(–1, 7)
(–1, 1)
(7, –2)

Answer 1

Translation T_{−4,3} maps (x,y) -> (x−4, y+3). Invert it: original = (x'+4, y'−3).

Compute:
- A' (−5,4) -> A = (−5+4, 4−3) = (−1,1)
- B' (3,4) -> B = (3+4, 4−3) = (7,1)
- C' (3,1) -> C = (3+4, 1−3) = (7,−2)
- D' (−5,1) -> D = (−5+4, 1−3) = (−1,−2)

Select: (−1,−2), (7,1), (−1,1), (7,−2).