Question

what is the mapping rule for a 180 degree rotation about the origin? (x,y)→(-y,-x) (x,y)→(-y,x) (x,y)→(-x,-y) (x,y)→(x,-y)

Explanation:

Step1: Recall rotation rules

When rotating a point \((x,y)\) \(180^{\circ}\) about the origin, we use the rule \((x,y)\to(-x,-y)\).
For example, if we have a point \((2,3)\), after \(180^{\circ}\) rotation about the origin, it becomes \((- 2,-3)\).

Step2: Analyze each option

• Option \((x,y)\to(-y,-x)\): This is a \(270^{\circ}\) counter - clockwise (or \(90^{\circ}\) clockwise) rotation rule.
• Option \((x,y)\to(-y,x)\): This is a \(90^{\circ}\) counter - clockwise rotation rule.
• Option \((x,y)\to(x,-y)\): This is a reflection over the \(x\) - axis rule.
• Option \((x,y)\to(-x,-y)\): This is the correct \(180^{\circ}\) rotation about the origin rule.

Answer:

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