Question

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

Explanation:

Step1: Find coordinates of F, G, H

From the graph:

• \( F(-8, 6) \)
• \( G(-8, 7) \) (Wait, correction: Looking at the grid, F is at (-8, 6)? Wait, no, let's recheck. Wait, the y-axis: F is at y=6? Wait, the grid lines: Let's see, F is at x=-8, y=6? Wait, G is at x=-8, y=7? Wait, H is at x=-4, y=5? Wait, maybe I misread. Wait, the y-axis has 10 at top. Let's check the coordinates:

Looking at the graph:

• Point F: x = -8, y = 6 (since it's 8 units left of y-axis, 6 up from x-axis)
• Point G: x = -8, y = 7 (same x as F, 1 unit up)
• Point H: x = -4, y = 5 (4 units left of y-axis, 5 up)

Step2: Apply reflection over y-axis

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

• For \( F(-8, 6) \): Reflect to \( F'(8, 6) \) (since -(-8)=8, y remains 6)
• For \( G(-8, 7) \): Reflect to \( G'(8, 7) \) ( -(-8)=8, y remains 7)
• For \( H(-4, 5) \): Reflect to \( H'(4, 5) \) ( -(-4)=4, y remains 5)

Step3: Plot the reflected points

Plot \( F'(8, 6) \), \( G'(8, 7) \), and \( H'(4, 5) \), then connect them to form the reflected triangle \( \triangle F'G'H' \).

Answer:

The image of \( \triangle FGH \) after reflection over the y - axis has vertices \( F'(8, 6) \), \( G'(8, 7) \), and \( H'(4, 5) \). (To graph, plot these points and connect them.)