Question

what is the image of (-4, -7) after a reflection over the x-axis?

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So, if we have a point \((x,y)\), after reflection over the \(x\) - axis, the image is \((x, - y)\).

Step2: Apply the rule to the given point

Given the point \((-4,-7)\), here \(x=-4\) and \(y = - 7\). When we reflect over the \(x\) - axis, the \(x\) - coordinate \(x=-4\) stays the same, and the \(y\) - coordinate becomes \(-y=-(-7) = 7\). So the image of the point \((-4,-7)\) after reflection over the \(x\) - axis is \((-4,7)\).

Answer:

\((-4,7)\)