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: Understand rotation rule

The notation $R_{0,180^{\circ}}$ means a rotation of 180 - degrees about the origin $(0,0)$.

Step2: Recall rotation formula

When a point $(x,y)$ is rotated 180 - degrees about the origin, the new coordinates $(x',y')$ are given by the transformation $(x,y)\to(-x,-y)$.

Answer:

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