Question

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

Explanation:

Step1: Identify coordinates of E, F, G, H

From the graph, we can find the coordinates:

• \( E(8, -8) \)
• \( F(9, -8) \)
• \( G(9, -7) \)
• \( H(8, -7) \)

Step2: Apply reflection over y - axis rule

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

• For \( E(8, -8) \): After reflection, \( E'(-8, -8) \)
• For \( F(9, -8) \): After reflection, \( F'(-9, -8) \)
• For \( G(9, -7) \): After reflection, \( G'(-9, -7) \)
• For \( H(8, -7) \): After reflection, \( H'(-8, -7) \)

Step3: Plot the reflected points

Plot the points \( E'(-8, -8) \), \( F'(-9, -8) \), \( G'(-9, -7) \), \( H'(-8, -7) \) on the coordinate plane and connect them to form the reflected square.

Answer:

The image of square \( EFGH \) after reflection over the \( y \) - axis has vertices at \( E'(-8, -8) \), \( F'(-9, -8) \), \( G'(-9, -7) \), \( H'(-8, -7) \) (plotted on the coordinate plane as described).