Question

which rule represents ( r_{0,180^{circ}} )?
( (x,y)\to(-y,x) )
( (x,y)\to(-x,-y) )
( (x,y)\to(y,-x) )
( (x,y)\to(y,x) )

Explanation:

Step1: Recall rotation rule

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

Step2: Analyze other options

• For \((x,y)\to(-y,x)\), it is a \(90^{\circ}\) counter - clockwise rotation.
• For \((x,y)\to(y,-x)\), it is a \(90^{\circ}\) clockwise rotation.
• For \((x,y)\to(y,x)\), it is a reflection over the line \(y = x\).

Answer:

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