Question

graph the image of quadrilateral vwxy after the following glide reflection: translation 17 units down reflection across the y - axis

Explanation:

Step1: Identify Original Coordinates

First, find the coordinates of vertices \( V, W, X, Y \) from the graph.

• \( V(-4, 12) \)
• \( W(-6, 6) \)
• \( X(-12, 8) \)
• \( Y(-14, 12) \)

Step2: Apply Translation (17 units down)

A translation 17 units down subtracts 17 from the \( y \)-coordinate.

• \( V'(-4, 12 - 17) = (-4, -5) \)
• \( W'(-6, 6 - 17) = (-6, -11) \)
• \( X'(-12, 8 - 17) = (-12, -9) \)
• \( Y'(-14, 12 - 17) = (-14, -5) \)

Step3: Apply Reflection (across \( y \)-axis)

Reflecting across the \( y \)-axis changes \( x \)-coordinate sign (\( (x, y) \to (-x, y) \)):

• \( V''(4, -5) \)
• \( W''(6, -11) \)
• \( X''(12, -9) \)
• \( Y''(14, -5) \)

Step4: Graph the Image

Plot points \( V''(4, -5) \), \( W''(6, -11) \), \( X''(12, -9) \), \( Y''(14, -5) \) and connect them to form the reflected quadrilateral.

Answer:

The image of quadrilateral \( VWXY \) after glide reflection has vertices at \( (4, -5) \), \( (6, -11) \), \( (12, -9) \), and \( (14, -5) \). (Graph these points to visualize the image.)