Question

the image of a point is given by the rule $r_{y = -x}(x,y)\to(-4,9)$. what are the coordinates of its pre - image? (-9,4) (-4,-9) (4,9) (9,-4)

Explanation:

Step1: Understand the reflection rule

The rule $r_{y = -x}(x,y)$ reflects a point across the line $y=-x$. The transformation rule for reflecting a point $(x,y)$ across the line $y =-x$ is $(x,y)\to(-y,-x)$.

Step2: Set up equations

We know that the image is $(-4,9)$. Let the pre - image be $(x,y)$. According to the rule $(x,y)\to(-y,-x)=(-4,9)$. So we have the system of equations: $-y=-4$ and $-x = 9$.

Step3: Solve the equations

From $-y=-4$, we get $y = 4$. From $-x=9$, we get $x=-9$.

Answer:

A. $(-9,4)$