Question

graph the image of r(1, 5) 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 given by \(R'(x,-y)\).

Step2: Identify the coordinates of point R

From the problem, the coordinates of point \(R\) are \((1,5)\).

Step3: Apply the reflection rule

Using the rule for reflection over the \(x\) - axis, for the point \(R(1,5)\), the \(x\) - coordinate \(x = 1\) remains unchanged, and the \(y\) - coordinate \(y = 5\) becomes \(-y=- 5\). So the coordinates of the image of \(R\) after reflection over the \(x\) - axis are \((1,-5)\). To graph this point, we locate \(x = 1\) on the \(x\) - axis and \(y=-5\) on the \(y\) - axis and mark the point.

Answer:

The image of \(R(1,5)\) after reflection over the \(x\) - axis is the point with coordinates \((1, - 5)\) (and its graph is the point at \(x = 1,y=-5\) on the coordinate plane).