Question

1. the segment xy with endpoints x(3, 1) and y(2, -2) is rotated such that x(-3, -1) and y(-2, 2). describe the rotation and represent it algebraically.

Explanation:

Step1: Analyze the coordinate change

For point \(X(3,1)\) to \(X'(-3,-1)\), \(x = 3\) becomes \(-3\) (\(x\to -x\)), \(y = 1\) becomes \(-1\) (\(y\to -y\)).
For point \(Y(2,-2)\) to \(Y'(-2,2)\), \(x = 2\) becomes \(-2\) (\(x\to -x\)), \(y=-2\) becomes \(2\) (\(y\to -y\)).

Step2: Recall rotation rules

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin, the rule is \((x,y)\to(-x,-y)\)

Answer:

The rotation is \(180^{\circ}\) about the origin. The algebraic representation is \((x,y)\to(-x,-y)\)