Question

graph the image of square pqrs after a reflection over the y-axis.

Explanation:

Step1: Identify original coordinates

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

• \( P(-9, -6) \)
• \( Q(-4, -6) \)
• \( R(-4, 0) \)
• \( S(-9, 0) \)

Step2: Apply reflection over y - axis rule

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

• For \( P(-9, -6) \): Reflect to \( P'(9, -6) \) (since \( -(-9)=9 \), \( y \)-coordinate remains \( -6 \))
• For \( Q(-4, -6) \): Reflect to \( Q'(4, -6) \) (since \( -(-4)=4 \), \( y \)-coordinate remains \( -6 \))
• For \( R(-4, 0) \): Reflect to \( R'(4, 0) \) (since \( -(-4)=4 \), \( y \)-coordinate remains \( 0 \))
• For \( S(-9, 0) \): Reflect to \( S'(9, 0) \) (since \( -(-9)=9 \), \( y \)-coordinate remains \( 0 \))

Step3: Graph the reflected points

Plot the points \( P'(9, -6) \), \( Q'(4, -6) \), \( R'(4, 0) \), and \( S'(9, 0) \) on the coordinate plane and connect them to form the reflected square.

Answer:

The image of square \( PQRS \) after reflection over the \( y \)-axis has vertices at \( P'(9, -6) \), \( Q'(4, -6) \), \( R'(4, 0) \), and \( S'(9, 0) \). (To graph, plot these points and connect them in order.)