Question

On a coordinate plane, a square and a point are shown. The square has points R prime (negative 8, 1), S prime (negative 4, 1), T prime (negative 4, negative 3), and U prime (negative 8, negative 3). Point S is at (3, negative 5).
Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU?

(–5, –3)
(3, –3)
(–1, –6)
(4, –9)

Answer 1

Translation vector v = S' - S = (−4−3, 1−(−5)) = (−7, 6).
Apply R = R' − v = (−8+7, 1−6) = (−1, −5). Similarly T = (3, −9), U = (−1, −9).
So pre-image square has sides x = −1, x = 3, y = −5, y = −9. The point (−1, −6) lies on the left side.

Answer: (−1, −6).