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 \((x,y)\to(x + 1,y-3)\).

Step2: Apply the inverse translation rule to \(B'\)

Since the translation rule is \((x,y)\to(x + 1,y-3)\), the inverse translation rule is \((x,y)\to(x - 1,y + 3)\).
For \(B'(-1,0)\), using the inverse rule:
\(x=-1-1=-2\) and \(y = 0+3=3\)

Answer:

\(B(-2,3)\)