Question

the point m(6, -6) is reflected over the x - axis. what are the coordinates of the resulting point, m?

Explanation:

Step1: Recall reflection over x - axis rule

When a point \((x,y)\) is reflected over the \(x\) - axis, the rule is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So the formula for the reflection of a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\).

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

For the point \(M(6,-6)\), the \(x\) - coordinate is \(6\) and the \(y\) - coordinate is \(-6\). Using the reflection rule over the \(x\) - axis, we keep the \(x\) - coordinate as \(6\) and change the sign of the \(y\) - coordinate. The new \(y\) - coordinate is \(-(-6)=6\). So the coordinates of the reflected point \(M'\) are \((6,6)\).

Answer:

\((6,6)\)