Question

identifying rules for rotations. 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

A rotation of 180 - degrees about the origin $(0,0)$ changes the sign of both the $x$ - coordinate and the $y$ - coordinate of a point $(x,y)$.

Step2: Identify correct rule

The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$.

Answer:

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