Question

On a coordinate plane, parallelogram A B C D has points (2, 4), (4, 4), (3, 2), (1, 2).

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

A''

B''(3, 2)

C''

D''

Answer 1

The vertices of the final image after the composite transformation T–1, –2 ◉ ry = x applied to parallelogram ABCD are A''(2, 1), B''(3, 2), C''(1, 2), and D''(0, 1).

Step-by-step explanation:

The question involves transforming the vertices of a parallelogram ABCD using a composite transformation. The transformation consists of a translation T–1, –2 followed by a reflection in the line y=x, denoted as ry=x.

Let's apply this transformation to each vertex:

For vertex A (2, 4):
1. Translate A by –1 in the x direction and –2 in the y direction: A' = (2–1, 4–2) = (1, 2).
2. Reflect A' over the line y=x: A'' = (2, 1).

Similarly, for B (4, 4), after applying T–1, –2 and ry=x, we get B'' = (4, 3).

Following these steps:

• Vertex C (3, 2) transforms to C'' (1, 2).
• Vertex D (1, 2) transforms to D'' (0, 1).

Thus, the vertices of the final image after the composite transformation are A''(2, 1), B''(3, 2), C''(1, 2), and D''(0, 1).