Question

write the coordinates of the vertices after a reflection over the x - axis.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex. From the graph:

• \( P(-7, -4) \)
• \( Q(-7, -1) \)
• \( R(-2, -1) \)
• \( S(-2, -4) \)

Step2: Apply reflection over x - axis

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

• For \( P(-7, -4) \): Apply the rule \( x=-7,y = - 4\), so \( P'(-7, -(-4))=(-7,4) \)
• For \( Q(-7, -1) \): Apply the rule \( x = - 7,y=-1\), so \( Q'(-7,-(-1))=(-7,1) \)
• For \( R(-2, -1) \): Apply the rule \( x=-2,y = - 1\), so \( R'(-2,-(-1))=(-2,1) \)
• For \( S(-2, -4) \): Apply the rule \( x=-2,y=-4\), so \( S'(-2,-(-4))=(-2,4) \)

Answer:

\( P'(-7, 4) \)
\( Q'(-7, 1) \)
\( R'(-2, 1) \)
\( S'(-2, 4) \)