Question

graph the image of r(10, -3) 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 \(R(x,y)\), after reflection over the \(x\) - axis, the image \(R'\) will have coordinates \((x, - y)\).

Step2: Identify the coordinates of point R

From the graph, the coordinates of point \(R\) are \((10,-3)\).

Step3: Apply the reflection rule

Using the rule for reflection over the \(x\) - axis, for the point \(R(10,-3)\), the \(x\) - coordinate \(x = 10\) remains unchanged, and the \(y\) - coordinate \(y=-3\) changes its sign. So the \(y\) - coordinate of the image \(R'\) will be \(-(-3)=3\). Thus, the coordinates of the image \(R'\) after reflection over the \(x\) - axis are \((10,3)\).

To graph this point, we find the location on the coordinate plane where \(x = 10\) and \(y = 3\) and plot the point.

Answer:

The image of \(R(10,-3)\) after reflection over the \(x\) - axis is the point with coordinates \((10,3)\).