Question

square abcd was translated using the rule (x,y)→(x - 4,y + 15) to form abcd. what are the coordinates of point d in the pre - image if the coordinates of point d in the image are (9, - 8)? (13, - 23) (5, 7) (18, 1) (-6, - 4)

Explanation:

Step1: Set up equations for x - coordinate

Let the pre - image coordinates be $(x,y)$ and the image coordinates be $(x',y')$. Given the translation rule $(x,y)\to(x - 4,y + 15)$ and $x'=9$. So $x-4 = 9$.
Solve for $x$: $x=9 + 4=13$.

Step2: Set up equations for y - coordinate

Given $y'=-8$, and the rule $y'=y + 15$. So $y+15=-8$.
Solve for $y$: $y=-8 - 15=-23$.

Answer:

$(13,-23)$