Question

graph the image of e(3, −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 \(E(x,y)=(3, - 3)\), after reflection over the \(x\) - axis, the new point \(E'\) will have coordinates \((x,-y)\).

Step2: Apply the rule to point \(E(3,-3)\)

For the point \(E(3,-3)\), \(x = 3\) and \(y=-3\). Using the reflection rule \((x,y)\to(x, - y)\), we substitute \(x = 3\) and \(y=-3\) into the rule. So, \(-y=-(-3)=3\). Therefore, the coordinates of the image of \(E(3,-3)\) after reflection over the \(x\) - axis are \((3,3)\).

To graph this point, we locate \(x = 3\) on the \(x\) - axis and \(y = 3\) on the \(y\) - axis and mark the point \((3,3)\) on the coordinate plane.

Answer:

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