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

Accepted Solution

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)