Question

graph the image of kite ghij after the following glide reflection;
translation 17 units up
reflection across the y-axis

Explanation:

Step1: Identify Coordinates of GHIJ

First, find the coordinates of each vertex of kite \( GHIJ \). From the graph:

• \( G(2, -4) \)
• \( H(2, -10) \)
• \( I(12, -14) \)
• \( J(8, -4) \)

Step2: Apply Translation 17 Units Up

A translation 17 units up changes the \( y \)-coordinate by adding 17. The transformation rule is \( (x, y) \to (x, y + 17) \).

• For \( G(2, -4) \): \( (2, -4 + 17) = (2, 13) \)
• For \( H(2, -10) \): \( (2, -10 + 17) = (2, 7) \)
• For \( I(12, -14) \): \( (12, -14 + 17) = (12, 3) \)
• For \( J(8, -4) \): \( (8, -4 + 17) = (8, 13) \)

Step3: Apply Reflection Across the \( y \)-axis

A reflection across the \( y \)-axis changes the \( x \)-coordinate to its opposite. The transformation rule is \( (x, y) \to (-x, y) \).

• For \( G(2, 13) \): \( (-2, 13) \)
• For \( H(2, 7) \): \( (-2, 7) \)
• For \( I(12, 3) \): \( (-12, 3) \)
• For \( J(8, 13) \): \( (-8, 13) \)

Step4: Graph the Transformed Vertices

Plot the points \( (-2, 13) \), \( (-2, 7) \), \( (-12, 3) \), and \( (-8, 13) \) on the coordinate plane and connect them to form the image of the kite after the glide reflection.

Answer:

The image of kite \( GHIJ \) after the glide reflection has vertices at \( (-2, 13) \), \( (-2, 7) \), \( (-12, 3) \), and \( (-8, 13) \). (Graph these points to visualize the transformed kite.)