Question

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

Explanation:

Step1: Find coordinates of original points

First, identify the coordinates of \( P \), \( Q \), and \( R \) from the graph.

• \( P \) is at \( (-10, -2) \)
• \( Q \) is at \( (-2, -2) \)
• \( R \) is at \( (-8, -5) \)

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 \( P(-10, -2) \): Applying the rule, we get \( P' = (10, -2) \) (since \( -(-10)=10 \) and \( y \)-coordinate remains \( -2 \))
• For \( Q(-2, -2) \): Applying the rule, we get \( Q' = (2, -2) \) (since \( -(-2) = 2 \) and \( y \)-coordinate remains \( -2 \))
• For \( R(-8, -5) \): Applying the rule, we get \( R' = (8, -5) \) (since \( -(-8)=8 \) and \( y \)-coordinate remains \( -5 \))

Step3: Plot the reflected points

Plot the points \( P'(10, -2) \), \( Q'(2, -2) \), and \( R'(8, -5) \) on the coordinate plane and connect them to form the reflected triangle \( \triangle P'Q'R' \).

Answer:

The image of \( \triangle PQR \) after reflection over the \( y \)-axis has vertices at \( P'(10, -2) \), \( Q'(2, -2) \), and \( R'(8, -5) \). (To graph it, plot these points and connect them.)