Question

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

Explanation:

Step1: Recall reflection rule

The rule $r_{y = -x}(x,y)=(-y,-x)$. Given the image point is $(-4,9)$.

Step2: Find pre - image

Let the pre - image be $(x,y)$. Then $(-y,-x)=(-4,9)$. So, $-y=-4$ gives $y = 4$ and $-x = 9$ gives $x=-9$.

Answer:

A. $(-9,4)$