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

Step2: Set up equations for pre - image

Let the pre - image be $(a,b)$. After reflection over $y=-x$, we have $(a,b)\to(-b,-a)$. Given the image is $(-4,9)$, so $-b=-4$ and $-a = 9$.

Step3: Solve for $a$ and $b$

From $-b=-4$, we get $b = 4$. From $-a=9$, we get $a=-9$.

Answer:

A. $(-9,4)$