Question

what is the image of $(-5,-1)$ after a reflection over the $x$-axis?

Explanation:

Step1: Recall the reflection rule over the x - axis

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

Step2: Apply the rule to the given point

For the point \((-5,-1)\), here \(x=-5\) and \(y = - 1\). Using the rule \((x,y)\to(x,-y)\), we substitute \(y=-1\) into \(-y\). So \(-y=-(-1)=1\).

Answer:

\((-5,1)\)