Question

graph the image of r(-2, 1) 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 \(R(x,y)\), its image \(R'\) after reflection over the \(x\) - axis is \((x, - y)\).

Step2: Apply the rule to point \(R(-2,1)\)

For the point \(R(-2,1)\), where \(x=-2\) and \(y = 1\), after reflection over the \(x\) - axis, the \(x\) - coordinate is still \(-2\) and the \(y\) - coordinate becomes \(-1\). So the image of \(R(-2,1)\) after reflection over the \(x\) - axis is the point \((-2,-1)\). To graph this point, we find the location on the coordinate plane with \(x=-2\) (2 units to the left of the origin on the \(x\) - axis) and \(y = - 1\) (1 unit below the \(x\) - axis).

Answer:

The image of \(R(-2,1)\) after reflection over the \(x\) - axis is the point \((-2,-1)\), and it should be graphed at the coordinates \((-2,-1)\) on the given coordinate plane.