Question

the point r(-1, -6) is reflected over the x-axis. what are the coordinates of the resulting point, r’?

Explanation:

Step1: Recall reflection over x - axis rule

When a point \((x,y)\) is reflected over the \(x\) - axis, the \(x\) - coordinate remains the same, and the \(y\) - coordinate changes its sign. 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 \(R(-1,-6)\)

For the point \(R(-1,-6)\), the \(x\) - coordinate \(x=-1\) will stay the same. The \(y\) - coordinate \(y = - 6\), when we change its sign, we get \(-y=-(-6) = 6\). So the coordinates of the reflected point \(R'\) are \((-1,6)\).

Answer:

\((-1,6)\)