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)? (-6, -4) (13, -23) (18, 1) (5, 7)

Explanation:

Step1: Set up equations for x - coordinate

Let the pre - image coordinates of point 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 \(9=x - 4\).

Step2: Solve for x

Add 4 to both sides of the equation \(9=x - 4\). So \(x=9 + 4=13\).

Step3: Set up equations for y - coordinate

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 \(-8=y + 15\).

Step4: Solve for y

Subtract 15 from both sides of the equation \(-8=y + 15\). So \(y=-8-15=-23\).

Answer:

\((13,-23)\)