Question

graph the image of trapezoid tuvw after a reflection over the line y = x.

Explanation:

Step1: Identify coordinates

First, find the coordinates of trapezoid \( TUVW \):

• \( T(-10, 0) \)
• \( U(-10, 8) \)
• \( V(-6, 2) \)
• \( W(-6, -2) \)

Step2: Apply reflection over \( y = x \)

The rule for reflecting a point \( (x, y) \) over the line \( y = x \) is \( (x, y) \to (y, x) \).

• For \( T(-10, 0) \): Reflect to \( T'(0, -10) \)
• For \( U(-10, 8) \): Reflect to \( U'(8, -10) \)
• For \( V(-6, 2) \): Reflect to \( V'(2, -6) \)
• For \( W(-6, -2) \): Reflect to \( W'(-2, -6) \)

Step3: Plot the reflected points

Plot \( T'(0, -10) \), \( U'(8, -10) \), \( V'(2, -6) \), and \( W'(-2, -6) \) on the coordinate plane and connect them to form the reflected trapezoid.

Answer:

The image of trapezoid \( TUVW \) after reflection over \( y = x \) has vertices at \( T'(0, -10) \), \( U'(8, -10) \), \( V'(2, -6) \), and \( W'(-2, -6) \). (Note: Since the problem asks to graph the image, the final answer involves plotting these points as described.)