Question

finding coordinates of a pre - image
triangle abc is translated to image abc. in this translation, a(5, 1) maps to a(6, - 2). the coordinates of b are (-1, 0). what are the coordinates of b?
b( , )

Explanation:

Step1: Find the translation rule

The translation from \(A(5,1)\) to \(A'(6, - 2)\) is \((x,y)\to(x + 1,y-3)\) since \(6-5 = 1\) (change in \(x\)-coordinate) and \(-2 - 1=-3\) (change in \(y\)-coordinate).

Step2: Reverse the translation for \(B'\)

If \(B'\) has coordinates \((-1,0)\), to find the pre - image \(B\), we reverse the translation. For the \(x\)-coordinate of \(B\): \(x=-1 - 1\). For the \(y\)-coordinate of \(B\): \(y=0+3\).

Answer:

\((-2,3)\)