Question

write the coordinates of the vertices after a reflection over the line y = x.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( D \): Looking at the grid, \( D \) is at \( (8, -9) \) (wait, no, let's check again. Wait, the vertical line for \( D \) is x=8, and the horizontal line is y=-9? Wait, no, the grid: from the graph, \( D \) is at (8, -9)? Wait, no, the yellow points: \( D \) is at (8, -9)? Wait, no, let's see the y-axis. Wait, the bottom is -10, so \( D \) is at (8, -9)? Wait, no, maybe I misread. Wait, the coordinates: \( D \) is (8, -9)? Wait, no, let's check the original points. Wait, \( D \), \( E \), \( F \), \( G \): \( G \) is at (8, 0), \( F \) is at (10, 0), \( E \) is at (10, -9), \( D \) is at (8, -9). Yes, that makes a rectangle. So original coordinates:
• \( D(8, -9) \)
• \( E(10, -9) \)
• \( F(10, 0) \)
• \( G(8, 0) \)

Step2: Reflect over \( y = x \)

The rule for reflecting a point \( (x, y) \) over the line \( y = x \) is to swap the x and y coordinates, so the new point is \( (y, x) \).

For \( D(8, -9) \):

Swap x and y: \( D'(-9, 8) \)

For \( E(10, -9) \):

Swap x and y: \( E'(-9, 10) \)

For \( F(10, 0) \):

Swap x and y: \( F'(0, 10) \)

For \( G(8, 0) \):

Swap x and y: \( G'(0, 8) \)

Answer:

\( D'(-9, 8) \)
\( E'(-9, 10) \)
\( F'(0, 10) \)
\( G'(0, 8) \)