Question

graph the image of △uvw after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of \( U \), \( V \), and \( W \) from the graph.

• \( U \) is at \( (2, -2) \)
• \( V \) is at \( (10, -2) \)
• \( W \) is at \( (1, -8) \)

Step2: Apply 180° rotation rule

The rule for a 180° counterclockwise (or clockwise) rotation around the origin is \( (x, y) \to (-x, -y) \).

For \( U(2, -2) \):

Apply the rule: \( (2, -2) \to (-2, 2) \)

For \( V(10, -2) \):

Apply the rule: \( (10, -2) \to (-10, 2) \)

For \( W(1, -8) \):

Apply the rule: \( (1, -8) \to (-1, 8) \)

Step3: Plot the new points

Plot the points \( U'(-2, 2) \), \( V'(-10, 2) \), and \( W'(-1, 8) \) on the coordinate plane and connect them to form the image of \( \triangle UVW \) after the 180° rotation.

Answer:

The image of \( \triangle UVW \) after a 180° counterclockwise rotation around the origin has vertices at \( U'(-2, 2) \), \( V'(-10, 2) \), and \( W'(-1, 8) \). (To graph, plot these points and connect them.)