Question

use coordinate notation to write the rule that maps each pre - image to its image. then identify the transformation. graph the image pqr to check your answer.
the coordinate rule is: (x,y)→
the transformation is:
preimage\timage
p( - 4,2)→p(4, - 2)
q( - 1,3)→q(1, - 3)
r( - 3, - 3)→r(3,3)
do the x, y or both x and y values change sign?
which rule on previous page does that happen with?

Explanation:

Step1: Analyze change in coordinates

For point $P(-4,2)$ to $P'(4, - 2)$, $x$ - coordinate changes from $-4$ to $4$ (sign changes) and $y$ - coordinate changes from $2$ to $-2$ (sign changes). Similarly for $Q(-1,3)$ to $Q'(1,-3)$ and $R(-3,-3)$ to $R'(3,3)$.

Step2: Write the coordinate - rule

The rule for the transformation is $(x,y)\to(-x,-y)$.

Step3: Identify the transformation

A transformation of the form $(x,y)\to(-x,-y)$ is a rotation of $180^{\circ}$ about the origin.

Answer:

The coordinate rule is: $(x,y)\to(-x,-y)$
The transformation is: Rotation of $180^{\circ}$ about the origin.