Question

graph the image of rectangle pqrs after a reflection over the line y = 1.

Explanation:

Step1: Identify coordinates of PQRS

First, find the coordinates of the vertices of rectangle \( PQRS \). From the graph:

• \( P(-9, -7) \)
• \( Q(-8, -7) \)
• \( R(-8, -1) \)
• \( S(-9, -1) \)

Step2: Recall reflection over \( y = k \)

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

Step3: Reflect each vertex

• For \( P(-9, -7) \):

New \( y \)-coordinate: \( 2 - (-7)=2 + 7 = 9 \). So \( P'(-9, 9) \).

• For \( Q(-8, -7) \):

New \( y \)-coordinate: \( 2 - (-7)=9 \). So \( Q'(-8, 9) \).

• For \( R(-8, -1) \):

New \( y \)-coordinate: \( 2 - (-1)=2 + 1 = 3 \). So \( R'(-8, 3) \).

• For \( S(-9, -1) \):

New \( y \)-coordinate: \( 2 - (-1)=3 \). So \( S'(-9, 3) \).

Step4: Plot the reflected points

Plot the points \( P'(-9, 9) \), \( Q'(-8, 9) \), \( R'(-8, 3) \), \( S'(-9, 3) \) and connect them to form the reflected rectangle.

Answer:

The image of rectangle \( PQRS \) after reflection over \( y = 1 \) has vertices \( P'(-9, 9) \), \( Q'(-8, 9) \), \( R'(-8, 3) \), \( S'(-9, 3) \). (To graph, plot these points and connect them in order.)