Question

square abcd was translated using the rule $(x,y)\to(x - 4,y + 15)$ 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: Analyze the translation rule for \(x\)-coordinate

The translation rule is \((x,y)\to(x - 4,y + 15)\). For the \(x\)-coordinate, if the image \(x\)-coordinate is \(x'\), then \(x'=x-4\). Given \(x' = 9\), we solve for \(x\): \(x=x'+4\). Substituting \(x' = 9\), we get \(x=9 + 4=13\).

Step2: Analyze the translation rule for \(y\)-coordinate

For the \(y\)-coordinate, if the image \(y\)-coordinate is \(y'\), then \(y'=y + 15\). Given \(y'=-8\), we solve for \(y\): \(y=y'-15\). Substituting \(y'=-8\), we get \(y=-8-15=-23\).

So the coordinates of point \(D\) in the pre - image are \((13,-23)\).

Answer:

A. (13, -23)