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?\
$(4,9)$\
$(-9,4)$\
$(9,-4)$\
$(-4,-9)$

Explanation:

Step1: Recall reflection rule

The reflection rule over the line \( y = -x \) is \( r_{y=-x}(x, y) \to (-y, -x) \). Let the pre - image be \( (x, y) \) and the image be \( (-4, 9) \).

Step2: Set up equations

From the rule \( -y=-4 \) and \( -x = 9 \).

Step3: Solve for x and y

For \( -y=-4 \), multiply both sides by - 1, we get \( y = 4 \). For \( -x=9 \), multiply both sides by - 1, we get \( x=-9 \). So the pre - image is \( (-9, 4) \).

Answer:

\((-9, 4)\)