Question

what are the coordinates of the image of vertex p after a reflection of ( r_{x\text{-axis}}(x, y) )? ( p(square, square) )
p(-7, -4)
s(4, -4)
q(-7, -10)
r(4, -10)

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \(r_{x - \text{axis}}(x,y)=(x,-y)\).

Step2: Identify coordinates of point P

From the graph, the coordinates of point \(P\) are \((-7,-4)\).

Step3: Apply the reflection rule

Using the rule \(r_{x - \text{axis}}(x,y)=(x,-y)\), for \(x = - 7\) and \(y=-4\), we substitute into the rule. So the \(x\) - coordinate remains the same (\(x=-7\)) and the \(y\) - coordinate is the negative of \(-4\), which is \(4\). So the coordinates of \(P'\) are \((-7,4)\).

Answer:

\(P'(-7,4)\)