Question

A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?

On a coordinate plane, a rectangle has points D prime (negative 1, 3), E prime (4, 3), F prime (4, 1), G prime (negative 1, 1).

On a coordinate plane, a rectangle has points D prime (negative 2, 5), E prime (3, 5), F prime (3, 3), G prime (negative 2, 3).

On a coordinate plane, a rectangle has points D prime (0, 2), E prime (5, 2), F prime (5, 0), G prime (0, 0).

On a coordinate plane, a rectangle has points D prime (negative 1, negative 1), E prime (4, negative 1), F prime (4, negative 3), G prime (negative 1, negative 3).

Answer 1

T_{-1,2} means add (-1, 2) to each point.
D' = (-1-1, 3+2) = (-2, 5)
E' = (4-1, 3+2) = (3, 5)
F' = (4-1, 1+2) = (3, 3)
G' = (-1-1, 1+2) = (-2, 3)

So the image is D'(-2,5), E'(3,5), F'(3,3), G'(-2,3).