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 = S' − S = (−4 − 3, 1 − (−5)) = (−7, 6).
Apply inverse translation to R',T',U' to get pre-image vertices:
R = (−8,1) − (−7,6) = (−1,−5)
S = (−4,1) − (−7,6) = (3,−5)
T = (−4,−3) − (−7,6) = (3,−9)
U = (−8,−3) − (−7,6) = (−1,−9)

Sides are x = −1 (y from −5 to −9), x = 3 (y from −5 to −9), y = −5 (x from −1 to 3), y = −9 (x from −1 to 3).
Only (−1,−6) lies on a side.