Question

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

Explanation:

Step1: Identify original coordinates

First, find the coordinates of rectangle \( KLMN \). From the graph:

• \( K(-4, -4) \)
• \( L(6, -4) \)
• \( M(6, -2) \)
• \( N(-4, -2) \)

Step2: Apply reflection over x - axis rule

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

• For \( K(-4, -4) \): New coordinate \( K'(-4, -(-4)) = (-4, 4) \)
• For \( L(6, -4) \): New coordinate \( L'(6, -(-4)) = (6, 4) \)
• For \( M(6, -2) \): New coordinate \( M'(6, -(-2)) = (6, 2) \)
• For \( N(-4, -2) \): New coordinate \( N'(-4, -(-2)) = (-4, 2) \)

Step3: Plot the new points

Plot the points \( K'(-4, 4) \), \( L'(6, 4) \), \( M'(6, 2) \), and \( N'(-4, 2) \) on the coordinate plane and connect them to form the reflected rectangle.

Answer:

The reflected rectangle \( K'L'M'N' \) has vertices at \( K'(-4, 4) \), \( L'(6, 4) \), \( M'(6, 2) \), and \( N'(-4, 2) \). (To graph it, plot these points and connect them in order.)