Question

graph the image of trapezoid stuv after a reflection over the line y = 1.

Explanation:

Step1: Find Coordinates of Vertices

First, identify the coordinates of trapezoid \( STUV \):

• \( S(-2, 4) \)
• \( T(-2, 9) \)
• \( U(6, 7) \)
• \( V(6, 5) \)

Step2: Reflect Over \( y = 1 \)

The formula for reflecting a point \( (x, y) \) over the line \( y = k \) is \( (x, 2k - y) \). Here, \( k = 1 \), so the new \( y \)-coordinate is \( 2(1) - y = 2 - y \).

• For \( S(-2, 4) \): New \( y = 2 - 4 = -2 \), so \( S'(-2, -2) \)
• For \( T(-2, 9) \): New \( y = 2 - 9 = -7 \), so \( T'(-2, -7) \)
• For \( U(6, 7) \): New \( y = 2 - 7 = -5 \), so \( U'(6, -5) \)
• For \( V(6, 5) \): New \( y = 2 - 5 = -3 \), so \( V'(6, -3) \)

Step3: Plot Reflected Points

Plot \( S'(-2, -2) \), \( T'(-2, -7) \), \( U'(6, -5) \), \( V'(6, -3) \) and connect them to form the reflected trapezoid.

Answer:

The reflected trapezoid has vertices at \( S'(-2, -2) \), \( T'(-2, -7) \), \( U'(6, -5) \), \( V'(6, -3) \). (Graph these points on the coordinate plane.)