Question

1. point ( a ) is plotted at ( (8,-2) ). use the graph to answer parts (a)-(c).

a. write the ordered pair of the reflection of point ( a ) across the ( x )-axis.

b. write the ordered pair of the reflection of point ( a ) across the ( y )-axis.

c. write the ordered pair of the reflection of point ( a ) across the ( x )-axis and then across the ( y )-axis.

Explanation:

Step1: Reflection across x - axis

When reflecting a point \((x,y)\) across the \(x\) - axis, the rule is \((x,y)\to(x, - y)\). Given \(A=(8,-2)\), then \(y=-2\) and \(-y = 2\). So the reflection is \((8,2)\).

Step2: Reflection across y - axis

When reflecting a point \((x,y)\) across the \(y\) - axis, the rule is \((x,y)\to(-x,y)\). Given \(A=(8,-2)\), then \(x = 8\) and \(-x=-8\). So the reflection is \((-8,-2)\).

Step3: Reflection across x - axis then y - axis

First, reflect \((8,-2)\) across the \(x\) - axis: \((8,-2)\to(8,2)\) (from Step1). Then reflect \((8,2)\) across the \(y\) - axis. Using the rule \((x,y)\to(-x,y)\), with \(x = 8\) and \(y = 2\), we get \((-8,2)\).

Answer:

a. \((8,2)\)
b. \((-8,-2)\)
c. \((-8,2)\)