Question

the coordinates of a point and its image are given. is the reflection over the x-axis or y-axis? (-7, -6) to (-7, 6)

Explanation:

Step1: Recall reflection rules

The rule for reflecting a point \((x,y)\) over the x - axis is \((x,y)\to(x, - y)\), and the rule for reflecting a point \((x,y)\) over the y - axis is \((x,y)\to(-x,y)\).

Step2: Analyze the given points

We are given the point \((-7,-6)\) and its image \((-7,6)\). Let the original point be \((x,y)=(-7,-6)\) and the image be \((x',y') = (-7,6)\).
Comparing with the reflection rules, we see that \(x=-7=x'\) and \(y = - 6\), \(y'=6=-y\) (since \(-y=-(-6) = 6\)). This matches the rule for reflection over the x - axis \((x,y)\to(x,-y)\).

Answer:

Reflection over the x - axis