Question

finding a pre - image using a rule
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?
(-4, -9)
(-9, 4)
(4, 9)
(9, -4)

Explanation:

Step1: Recall reflection rule

The rule $r_{y = -x}(x,y)\to(-y,-x)$ represents a reflection over the line $y=-x$.

Step2: Apply the inverse - rule

If the image is $(-4,9)$, to find the pre - image, we use the inverse operation. Let the pre - image be $(x,y)$. According to the rule $(-y,-x)=(-4,9)$. So, $-y=-4$ and $-x = 9$. Solving for $x$ and $y$, we get $y = 4$ and $x=-9$.

Answer:

B. $(-9,4)$