Question

graph the image of u(-6, -7) 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 \((x,y)\), after reflection over the \(x\) - axis, the new point \((x',y')\) is given by \(x'=x\) and \(y'=-y\).

Step2: Apply the rule to point \(U(-6,-7)\)

For the point \(U(-6,-7)\), the \(x\) - coordinate \(x = - 6\) will remain the same. The \(y\) - coordinate \(y=-7\), so the new \(y\) - coordinate \(y'=-(-7) = 7\). So the image of \(U(-6,-7)\) after reflection over the \(x\) - axis is the point \((-6,7)\). To graph this point, we find the location on the coordinate plane where \(x=-6\) (6 units to the left of the origin on the \(x\) - axis) and \(y = 7\) (7 units above the origin on the \(y\) - axis) and plot the point.

Answer:

The image of \(U(-6,-7)\) after reflection over the \(x\) - axis is the point \((-6,7)\) (and it should be graphed at the coordinates \((-6,7)\) on the given coordinate plane).