Question

write the coordinates of the vertices after a reflection over the y - axis.
f((□,□))
g((□,□))
h((□,□))

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( F \), \( G \), and \( H \) from the graph.

• \( F \): Looking at the graph, \( F \) is at \( (-5, 1) \) (since it's 5 units left on the x - axis and 1 unit up on the y - axis).
• \( G \): \( G \) is at \( (-1, 1) \) (1 unit left on the x - axis and 1 unit up on the y - axis).
• \( H \): \( H \) is at \( (-9, -3) \) (9 units left on the x - axis and 3 units down on the y - axis).

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 \( F(-5,1) \):

Using the rule, \( x=-5 \), so \( -x = 5 \), and \( y = 1 \). So \( F'=(5,1) \).

• For \( G(-1,1) \):

Using the rule, \( x=-1 \), so \( -x = 1 \), and \( y = 1 \). So \( G'=(1,1) \).

• For \( H(-9,-3) \):

Using the rule, \( x=-9 \), so \( -x = 9 \), and \( y=-3 \). So \( H'=(9,-3) \).

Answer:

\( F'(5, 1) \)
\( G'(1, 1) \)
\( H'(9, -3) \)