Question

graph the image of $\triangle fgh$ after a reflection over the $y$-axis.

Explanation:

Step1: Find Coordinates of F, G, H

First, identify the coordinates of the vertices of \( \triangle FGH \). From the graph:

• \( F \): \( (-8, 6) \)
• \( G \): \( (-8, 7) \) (assuming the y - coordinate of G is 7, as it's one unit above F)
• \( H \): \( (-4, 5) \)

Step2: Apply Reflection Over y - axis

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

• For \( F(-8,6) \): After reflection, \( F'=(8,6) \)
• For \( G(-8,7) \): After reflection, \( G'=(8,7) \)
• For \( H(-4,5) \): After reflection, \( H'=(4,5) \)

Step3: Plot the Reflected Points

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

Answer:

The reflected triangle \( \triangle F'G'H' \) has vertices at \( (8,6) \), \( (8,7) \), and \( (4,5) \) (the graph should show these points connected, with \( F' \) and \( G' \) vertically aligned at \( x = 8 \), and \( H' \) at \( x = 4,y = 5 \), forming a triangle congruent to \( \triangle FGH \) but on the right - hand side of the y - axis).