Question

an image is drawn of a figure. after a 180° (counterclockwise) rotation about the origin, p(7, -2) is mapped to p (-7,2). identify the rule that maps p to p. (1 point) (x,y)→(x, y) (x,y)→(y, x) (x,y)→(-y, -x) (x,y)→(-x, -y)

Explanation:

Step1: Recall rotation rule

For a 180 - degree counter - clockwise rotation about the origin, the general rule for transforming a point $(x,y)$ is to change the sign of both the $x$ and $y$ coordinates.

Step2: Apply rule to point

Given point $P(7, - 2)$, when we apply the rule $(x,y)\to(-x,-y)$, we get $P'(-7,2)$ which matches the given transformation.

Answer:

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