Question

graph the image of kite pqrs after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Identify coordinates of vertices

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

• \( P(4, -10) \)
• \( Q(7, -4) \)
• \( R(4, -3) \)
• \( S(1, -4) \)

Step2: Apply 180° rotation rule

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

• For \( P(4, -10) \): \( (-4, 10) \)
• For \( Q(7, -4) \): \( (-7, 4) \)
• For \( R(4, -3) \): \( (-4, 3) \)
• For \( S(1, -4) \): \( (-1, 4) \)

Step3: Plot the new vertices

Plot the points \( P'(-4, 10) \), \( Q'(-7, 4) \), \( R'(-4, 3) \), and \( S'(-1, 4) \) on the coordinate plane and connect them to form the image of the kite after rotation.

Answer:

The image of kite \( PQRS \) after a \( 180^\circ \) counterclockwise rotation around the origin has vertices at \( P'(-4, 10) \), \( Q'(-7, 4) \), \( R'(-4, 3) \), and \( S'(-1, 4) \). (To graph, plot these points and connect them in order.)