Question

graph the image of trapezoid tuvw after a reflection over the y-axis.

Explanation:

Step1: Identify coordinates of vertices

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

• \( T(-10, -4) \)
• \( U(-10, 0) \)
• \( V(-7, 2) \)
• \( W(-7, -6) \)

Step2: Apply reflection over \( y \)-axis

The rule for reflection over the \( y \)-axis is \( (x, y) \to (-x, y) \). Apply this to each vertex:

• For \( T(-10, -4) \): \( (-(-10), -4) = (10, -4) \)
• For \( U(-10, 0) \): \( (-(-10), 0) = (10, 0) \)
• For \( V(-7, 2) \): \( (-(-7), 2) = (7, 2) \)
• For \( W(-7, -6) \): \( (-(-7), -6) = (7, -6) \)

Step3: Plot the new vertices

Plot the points \( T'(10, -4) \), \( U'(10, 0) \), \( V'(7, 2) \), \( W'(7, -6) \) and connect them to form the reflected trapezoid.

Answer:

The reflected trapezoid has vertices at \( (10, -4) \), \( (10, 0) \), \( (7, 2) \), and \( (7, -6) \). (Graphing these points on the coordinate plane completes the reflection.)