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 \((x,y)\). The translation rule for the x - coordinate is \(x'=x - 4\), where \(x'\) is the x - coordinate of the image. Given \(x' = 9\), we have the equation \(9=x - 4\).
Solve for \(x\): \(x=9 + 4=13\).

Step2: Set up y - coordinate equation

The translation rule for the y - coordinate is \(y'=y + 15\), where \(y'\) is the y - coordinate of the image. Given \(y'=-8\), we have the equation \(-8=y + 15\).
Solve for \(y\): \(y=-8 - 15=-23\).

Answer:

(13, -23)