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 point D be $(x,y)$. The translation rule for the x - coordinate is $x'=x - 4$. Given $x' = 9$, we have the equation $9=x - 4$.

Step2: Solve for x

Add 4 to both sides of the equation $9=x - 4$. So, $x=9 + 4=13$.

Step3: Set up y - coordinate equation

The translation rule for the y - coordinate is $y'=y + 15$. Given $y'=-8$, we have the equation $-8=y + 15$.

Step4: Solve for y

Subtract 15 from both sides of the equation $-8=y + 15$. So, $y=-8-15=-23$.

Answer:

$(13,-23)$