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: Define variables for pre - image coordinates

Let the coordinates of point \(D\) (pre - image) be \((x,y)\). The translation rule is \((x,y)\to(x - 4,y + 15)\), and the coordinates of \(D'\) (image) are \((9,-8)\).

Step2: Solve for \(x\) - coordinate

Using the \(x\) - component of the translation rule: \(x-4 = 9\). To find \(x\), we add 4 to both sides of the equation. So, \(x=9 + 4=13\).

Step3: Solve for \(y\) - coordinate

Using the \(y\) - component of the translation rule: \(y + 15=-8\). To find \(y\), we subtract 15 from both sides of the equation. So, \(y=-8-15=-23\).

Answer:

\((13,-23)\)