Question

Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y – 3.5) to create the image ΔA'B'C' shown on the coordinate plane.

Which graph shows the pre-image, ΔABC?

On a coordinate plane, a triangle has points A prime (negative 1, 2), B prime (1, negative 1), C prime (negative 5, negative 1).
On a coordinate plane, a triangle has points A (0.5, negative 1.5), B (0.5, negative 4.5), C (negative 3.5, negative 4.5).
On a coordinate plane, a triangle has points A (2.5, 0.5), B (2.5, 2.5), C (negative 1.5, negative 2.5).
On a coordinate plane, a triangle has points A (negative 4.5, 3.5), B (negative 4.5, 0.5), C (negative 8.5, 0.5).
On a coordinate plane, a triangle has points A (negative 2.5, 5.5), B (negative 2.5, 2.5), C (negative 6.5, 2.5).

Answer 1

Undo the translation: (x,y) = (x' − 1.5, y' + 3.5).

A'(-1, 2) → A = (-1 − 1.5, 2 + 3.5) = (-2.5, 5.5)
B'(1, -1) → B = (1 − 1.5, -1 + 3.5) = (-0.5, 2.5)
C'(-5, -1) → C = (-5 − 1.5, -1 + 3.5) = (-6.5, 2.5)

So the pre-image should have A(-2.5, 5.5), B(-0.5, 2.5), C(-6.5, 2.5). The only given graph that matches A and C (and is clearly the intended choice) is the one with A(-2.5, 5.5), B(-2.5, 2.5), C(-6.5, 2.5) — choose that graph (note: B's x-coordinate in the choices looks like a typo; the correct B is at x = -0.5).