Question

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

Explanation:

Step1: Identify coordinates

First, find the coordinates of each vertex of kite \( PQRS \):

• \( P(-6, -1) \)
• \( Q(-4, 0) \)
• \( R(-6, 5) \)
• \( S(-8, 0) \)

Step2: Apply reflection over y-axis

The rule for reflecting a point \((x, y)\) over the \( y \)-axis is \((x, y) \to (-x, y)\). Apply this to each vertex:

• For \( P(-6, -1) \): \( (-(-6), -1) = (6, -1) \)
• For \( Q(-4, 0) \): \( (-(-4), 0) = (4, 0) \)
• For \( R(-6, 5) \): \( (-(-6), 5) = (6, 5) \)
• For \( S(-8, 0) \): \( (-(-8), 0) = (8, 0) \)

Step3: Plot the new points

Plot the reflected points \( P'(6, -1) \), \( Q'(4, 0) \), \( R'(6, 5) \), and \( S'(8, 0) \) on the coordinate plane and connect them to form the reflected kite.

Answer:

The image of kite \( PQRS \) after reflection over the \( y \)-axis has vertices at \( P'(6, -1) \), \( Q'(4, 0) \), \( R'(6, 5) \), and \( S'(8, 0) \). (Graphing these points and connecting them forms the reflected kite.)