Question

Analyze the pre-image ABCD. What are the vertices of the final image if T–1, –2 ◦ ry = x is applied to figure ABCD?

Answer 1

Answer:

A''

(3,0)

B''

(3, 2)

C''

(1,1)

D''

(1, -1)

just making sure nobody puts the wrong answer!

Answer 2

Answers:

A''(3, 0); B''(3, 2); C''(1, 1); D''(1, -1)

Explanation:

We perform the reflection across y=x first.  This reflection switches the x- and y-coordinates; this maps:

A(2, 4)→A'(4, 2)

B(4, 4)→B'(4, 4)

C(3, 2)→C'(2, 3)

D(1, 2)→D'(2, 1)

Next we perform the translation.  This translation shifts the figure 1 unit left and 2 units down, by subtracting 1 from the x-coordinate and 2 from the y-coordinate.  This maps:

A'(4, 2)→A''(3, 0)

B'(4, 4)→B''(3, 2)

C'(2, 3)→C''(1, 1)

D'(2, 1)→D''(1, -1)