Question

the line 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. (x,y)→( )

Explanation:

Step1: Analyze the coordinate transformation

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

Step2: Determine the rotation rule

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

Answer:

\((x,y)\to(-x,-y)\)