Question

graph the image of d(4, -8) 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 \((x,y)\to(x, - y)\).

Step2: Apply the rule to point \(D(4,-8)\)

For the point \(D(4,-8)\), where \(x = 4\) and \(y=-8\), when we reflect it over the \(x\) - axis, we keep the \(x\) - coordinate the same and change the sign of the \(y\) - coordinate. So the new \(y\) - coordinate is \(-(-8)=8\). So the image of \(D(4,-8)\) after reflection over the \(x\) - axis is \((4,8)\). To graph this point, we find the location on the coordinate plane where \(x = 4\) (4 units to the right of the origin on the \(x\) - axis) and \(y = 8\) (8 units up from the origin on the \(y\) - axis) and plot the point.

Answer:

The image of \(D(4,-8)\) after reflection over the \(x\) - axis is the point \((4,8)\), which should be plotted at the coordinates \((4,8)\) on the given coordinate grid.