Question

1. what is the result of a reflection over the x - axis followed by a reflection over the y - axis?

a rotation of 180 degrees
a reflection over the y - axis
translations of equal distances
a reflection over the x - axis

Explanation:

Step1: Analyze reflection over x - axis

Let a point \((x,y)\) be reflected over the \(x\) - axis. The transformation rule is \((x,y)\to(x, - y)\).

Step2: Analyze reflection over y - axis

Let the point \((x,-y)\) (after reflection over \(x\) - axis) be reflected over the \(y\) - axis. The transformation rule is \((x,-y)\to(-x,-y)\).

Step3: Analyze rotation of \(180^{\circ}\)

The rule for a rotation of \(180^{\circ}\) about the origin is \((x,y)\to(-x,-y)\).

Answer:

A. A rotation of 180 degrees