Question

graph the image of k(8, -6) 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 \(K(x,y)\), its image \(K'\) after reflection over the \(x\) - axis is given by \(K'(x,-y)\).

Step2: Apply the rule to point \(K(8,-6)\)

For the point \(K(8,-6)\), the \(x\) - coordinate \(x = 8\) and the \(y\) - coordinate \(y=-6\). Using the reflection rule, the \(x\) - coordinate of the image will be the same as that of \(K\), i.e., \(x' = 8\), and the \(y\) - coordinate of the image \(y'=-y=-(-6) = 6\). So the image of \(K(8,-6)\) after reflection over the \(x\) - axis is \(K'(8,6)\).

Step3: Locate the image on the graph

To graph the point \(K'(8,6)\), we move 8 units to the right along the \(x\) - axis (since \(x = 8\)) and 6 units up along the \(y\) - axis (since \(y = 6\)) from the origin \((0,0)\).

Answer:

The image of \(K(8,-6)\) after reflection over the \(x\) - axis is the point \((8,6)\), which is located 8 units to the right on the \(x\) - axis and 6 units up on the \(y\) - axis.