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 the vertices of kite \( GHIJ \). From the graph:

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

Step2: Apply Translation (17 units up)

To translate a point \( (x, y) \) 17 units up, we add 17 to the \( y \)-coordinate. The translation rule is \( (x, y) \to (x, y + 17) \).

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

Step3: Apply Reflection across y - axis

To reflect a point \( (x, y) \) across the \( y \)-axis, we change the sign of the \( x \)-coordinate. The reflection rule is \( (x, y) \to (-x, y) \).

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

Step4: Graph the New Vertices

Plot the points \( G''(-2, 13) \), \( H''(-2, 7) \), \( I''(-12, 3) \), and \( J''(-8, 13) \) 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 \( G''(-2, 13) \), \( H''(-2, 7) \), \( I''(-12, 3) \), and \( J''(-8, 13) \). (To graph, plot these points and connect them in order.)