Question

the coordinates of a point and its image are given. is the reflection over the x-axis or y-axis? (-2, -6) to (2, -6)

Explanation:

Step1: Recall reflection rules

For reflection over the \(x\)-axis: If a point \((x,y)\) is reflected over the \(x\)-axis, the image is \((x, -y)\). For reflection over the \(y\)-axis: If a point \((x,y)\) is reflected over the \(y\)-axis, the image is \((-x, y)\).

Step2: Analyze the given points

The original point is \((-2, -6)\) and the image is \((2, -6)\). Let's compare with the reflection rules.

• For \(x\)-axis reflection: The \(y\)-coordinate should change sign. Here, the \(y\)-coordinate \(-6\) remains \(-6\), so not \(x\)-axis reflection.
• For \(y\)-axis reflection: The \(x\)-coordinate changes sign. The original \(x\)-coordinate is \(-2\), and the image \(x\)-coordinate is \(2\) (which is \(-(-2)\)), and the \(y\)-coordinate \(-6\) remains the same. This matches the \(y\)-axis reflection rule.

Answer:

Reflection over the \(y\)-axis