Question

a pentagon is transformed according to the rule ( r_{0,180^{circ}} ). which is another way to state the transformation?
( (x,y)\to(-x,-y) )
( (x,y)\to(-y - x) )
( (x,y)\to(x,-y) )
( (x,y)\to(-x,y) )

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin \((0,0)\), the new coordinates \((x',y')\) can be found using the rule.

Step2: Apply the rotation formula

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

Answer:

\((x,y)\to(-x,-y)\) (the first option)