Question

1. parallelogram rstu in the line y = x

Explanation:

Step1: Identify Coordinates

First, find the coordinates of points \( R \), \( S \), \( T \), \( U \). From the grid:

• \( R(-2, 3) \)
• \( S(2, 4) \)
• \( T(2, -2) \)
• \( U(-2, -3) \)

Step2: Reflect Over \( y = x \)

The reflection of a point \( (a, b) \) over \( y = x \) is \( (b, a) \). Apply this to each point:

• \( R' (3, -2) \)
• \( S' (4, 2) \)
• \( T' (-2, 2) \)
• \( U' (-3, -2) \)

Step3: Plot Reflected Points

Plot \( R' \), \( S' \), \( T' \), \( U' \) on the grid to get the reflected parallelogram.

Answer:

The reflected parallelogram \( R'S'T'U' \) has vertices at \( (3, -2) \), \( (4, 2) \), \( (-2, 2) \), \( (-3, -2) \). (To draw, connect these points in order.)