Question

graph the image of kite rstu after a reflection over the line y = -x.

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of the vertices of kite \( RSTU \). From the graph:

• \( R \): \( (0, -10) \)
• \( S \): \( (4, -8) \)
• \( T \): \( (1, -6) \)
• \( U \): \( (0, -8) \)

Step2: Apply reflection over \( y = -x \)

The rule for reflecting a point \( (x, y) \) over the line \( y = -x \) is \( (x, y) \to (-y, -x) \).

• For \( R(0, -10) \): Apply the rule: \( (-(-10), -0) = (10, 0) \)
• For \( S(4, -8) \): Apply the rule: \( (-(-8), -4) = (8, -4) \)
• For \( T(1, -6) \): Apply the rule: \( (-(-6), -1) = (6, -1) \)
• For \( U(0, -8) \): Apply the rule: \( (-(-8), -0) = (8, 0) \)

Step3: Plot the reflected points

Plot the new points \( R'(10, 0) \), \( S'(8, -4) \), \( T'(6, -1) \), \( U'(8, 0) \) on the coordinate plane and connect them to form the reflected kite.

Answer:

The reflected kite has vertices at \( R'(10, 0) \), \( S'(8, -4) \), \( T'(6, -1) \), and \( U'(8, 0) \). (To graph, plot these points and connect them in order.)