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, - 6)?
○ (13, - 22)
○ (5, 7)
○ (13, 1)
○ (- 6, - 4)

Explanation:

Step1: Recall the translation rule

The translation rule is \((x, y) \to (x - 4, y + 15)\). Let the coordinates of point \(D\) (pre - image) be \((x,y)\) and the coordinates of point \(D'\) (image) be \((x',y')=(9, - 7)\).
From the translation rule, we know that \(x'=x - 4\) and \(y'=y + 15\).

Step2: Solve for \(x\)

We know that \(x'=x - 4\) and \(x' = 9\). So we can solve the equation \(9=x - 4\) for \(x\).
Adding 4 to both sides of the equation \(9=x - 4\), we get \(x=9 + 4=13\).

Step3: Solve for \(y\)

We know that \(y'=y + 15\) and \(y'=-7\). So we can solve the equation \(-7=y + 15\) for \(y\).
Subtracting 15 from both sides of the equation \(-7=y + 15\), we get \(y=-7-15=-22\).

So the coordinates of point \(D\) in the pre - image are \((13,-22)\).

Answer:

(13, -22)