Question

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

Explanation:

Step1: Find coordinates of square vertices

First, identify the coordinates of the vertices of square \( QRST \). From the graph:

• \( Q \): \( (7, 3) \)
• \( R \): \( (9, 3) \)
• \( S \): \( (9, 5) \)
• \( T \): \( (7, 5) \)

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 \( Q(7, 3) \): After reflection, \( Q'(-7, 3) \)
• For \( R(9, 3) \): After reflection, \( R'(-9, 3) \)
• For \( S(9, 5) \): After reflection, \( S'(-9, 5) \)
• For \( T(7, 5) \): After reflection, \( T'(-7, 5) \)

Step3: Plot the reflected points

Plot the points \( Q'(-7, 3) \), \( R'(-9, 3) \), \( S'(-9, 5) \), and \( T'(-7, 5) \) on the coordinate plane and connect them to form the reflected square.

Answer:

The reflected square \( Q'R'S'T' \) has vertices at \( (-7, 3) \), \( (-9, 3) \), \( (-9, 5) \), and \( (-7, 5) \) (plotted on the coordinate plane as per the reflection rule).