Question

1. considering rotational transformation on a coordinate plane, how many degrees rotation will a point (x, y) around the origin end up at the point (-x, -y)? 180 degrees 90 degrees 360 degrees 270 degrees

Explanation:

Step1: Recall rotation rules

For a \(180^{\circ}\) rotation about the origin, the transformation rule is \((x,y)\to(-x, -y)\).
For a \(90^{\circ}\) rotation about the origin, if it is counter - clockwise, the rule is \((x,y)\to(-y,x)\); if it is clockwise, the rule is \((x,y)\to(y, -x)\).
For a \(360^{\circ}\) rotation about the origin, the rule is \((x,y)\to(x,y)\).
For a \(270^{\circ}\) rotation about the origin, if it is counter - clockwise, the rule is \((x,y)\to(y, -x)\); if it is clockwise, the rule is \((x,y)\to(-y,x)\).

Answer:

180 degrees