Question

1. match each transformation with the correct description

a. (x,y)→(−x,−y) ____ reflection across the y - axis
b. (x,y)→(−x,y) ____ rotation of 180° about the origin
c. (x,y)→(x,−y) ____ reflection across the x - axis.

Explanation:

Step1: Recall transformation rules

In a coordinate - plane, for a point \((x,y)\), different transformations have specific rules.

Step2: Analyze transformation A

For the transformation \((x,y)\to(-x, -y)\), when we change the sign of both \(x\) and \(y\) coordinates, it is a rotation of \(180^{\circ}\) about the origin.

Step3: Analyze transformation B

For the transformation \((x,y)\to(-x,y)\), changing the sign of the \(x\) - coordinate while keeping the \(y\) - coordinate the same is a reflection across the \(y\) - axis.

Step4: Analyze transformation C

For the transformation \((x,y)\to(x, -y)\), changing the sign of the \(y\) - coordinate while keeping the \(x\) - coordinate the same is a reflection across the \(x\) - axis.

Answer:

A. rotation of \(180^{\circ}\) about the origin
B. reflection across the \(y\) - axis
C. reflection across the \(x\) - axis