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…

Answer:

A. (-9, 4)

Explanation:

Step1: Understand the reflection rule

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

Step2: Set up equations

Let the pre - image be $(x,y)$ and the image be $(-4,9)$. According to the rule $(x,y)\to(-y,-x)$, we have $-y=-4$ and $-x = 9$.

Step3: Solve for $x$ and $y$

From $-y=-4$, we get $y = 4$. From $-x=9$, we get $x=-9$. So the pre - image is $(-9,4)$.