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

Answer

Explanation:

Step1: Identify coordinates of ABCD

First, find coordinates of each vertex. From the graph:

( A(-9, -10) ), ( B(-6, -10) ), ( C(-6, -3) ), ( D(-9, -3) )

Step2: Apply reflection over x - axis

The rule for reflection over the x - axis is ( (x, y) \to (x, -y) ).

For ( A(-9, -10) ): ( (-9, -(-10)) = (-9, 10) )
For ( B(-6, -10) ): ( (-6, -(-10)) = (-6, 10) )
For ( C(-6, -3) ): ( (-6, -(-3)) = (-6, 3) )
For ( D(-9, -3) ): ( (-9, -(-3)) = (-9, 3) )

Step3: Plot the reflected points

Plot ( A'(-9, 10) ), ( B'(-6, 10) ), ( C'(-6, 3) ), ( D'(-9, 3) ) and connect them to form the reflected rectangle.

(Note: Since the task is to graph, the key is finding reflected coordinates. The final graph will have vertices at ( (-9,10) ), ( (-6,10) ), ( (-6,3) ), ( (-9,3) ), forming a rectangle above the x - axis, mirroring the original below the x - axis.)

Answer:

The reflected rectangle ( A'B'C'D' ) has vertices at ( A'(-9, 10) ), ( B'(-6, 10) ), ( C'(-6, 3) ), ( D'(-9, 3) ). (To graph, plot these points and connect them in order.)