Question

graph the image of rectangle rstu after a reflection over the x-axis.

Explanation:

Step1: Find coordinates of original points

First, identify the coordinates of rectangle \( RSTU \):

• \( R(-9, -9) \)
• \( S(-2, -9) \)
• \( T(-2, -3) \)
• \( U(-9, -3) \)

Step2: Apply reflection over x - axis rule

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

• For \( R(-9, -9) \): New coordinate \( R'(-9, -(-9)) = (-9, 9) \)
• For \( S(-2, -9) \): New coordinate \( S'(-2, -(-9)) = (-2, 9) \)
• For \( T(-2, -3) \): New coordinate \( T'(-2, -(-3)) = (-2, 3) \)
• For \( U(-9, -3) \): New coordinate \( U'(-9, -(-3)) = (-9, 3) \)

Step3: Plot the new points

Plot the points \( R'(-9, 9) \), \( S'(-2, 9) \), \( T'(-2, 3) \), and \( U'(-9, 3) \) on the coordinate plane and connect them to form the reflected rectangle.

Answer:

The reflected rectangle \( R'S'T'U' \) has vertices at \( R'(-9, 9) \), \( S'(-2, 9) \), \( T'(-2, 3) \), and \( U'(-9, 3) \). (To graph it, plot these points and connect them in order.)