Question

graph the image of p(4, 1) after a reflection over the x-axis.

Explanation:

Step1: Recall the reflection rule

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

Step2: Apply the rule to the point \(P(4,1)\)

Here \(x = 4\) and \(y=1\). Using the rule \((x,y)\to(x, - y)\), we substitute \(y = 1\) into \(-y\). So the \(y -\)coordinate of the reflected point is \(-1\) and the \(x -\)coordinate remains \(4\).

Answer:

The image of \(P(4,1)\) after reflection over the \(x -\)axis is \(P'(4,-1)\).