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 x - coordinate equation

Let the pre - image coordinates of D be $(x,y)$. Given the translation rule $(x,y)\to(x - 4,y + 15)$ and the image point $D'(9,-8)$. For the x - coordinate, we have the equation $x-4 = 9$.
Solve for $x$: $x=9 + 4=13$.

Step2: Set up y - coordinate equation

For the y - coordinate, we have the equation $y + 15=-8$.
Solve for $y$: $y=-8-15=-23$.

Answer:

$(13,-23)$