Question

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 x - coordinate of A changes from 5 to 6, so the change in x is \(6 - 5=1\). The y - coordinate of A changes from 1 to - 2, so the change in y is \(-2 - 1=-3\). The translation rule is \((x,y)\to(x + 1,y-3)\).

Step2: Reverse the translation for B'

Let the coordinates of B be \((x,y)\). We know that for the translation \((x,y)\to(x + 1,y - 3)\) gives B'(-1,0). To find x, we set \(x+1=-1\), then \(x=-1 - 1=-2\). To find y, we set \(y-3 = 0\), then \(y=3\).

Answer:

\((-2,3)\)