Question

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

Explanation:

Step1: Identify original coordinates

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

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

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 \( P(-10, -2) \): Apply the rule, \( x=-10\), so \(-x = 10\). The image \( P' \) is \((10, -2)\).
• For \( Q(-2, -2) \): Apply the rule, \( x = - 2\), so \(-x=2\). The image \( Q' \) is \((2, -2)\).
• For \( R(-8, -5) \): Apply the rule, \( x=-8\), so \(-x = 8\). The image \( R' \) is \((8, -5)\).

Step3: Graph the new 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, plot these points and connect them.)