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 translation rule

To find the translation rule, we subtract the coordinates of $A$ from the coordinates of $A'$. Let the translation be $(x,y)\to(x + a,y + b)$. For the $x$-coordinate: $6-5=a$, so $a = 1$. For the $y$-coordinate: $- 2-1=b$, so $b=-3$. The translation rule is $(x,y)\to(x + 1,y-3)$.

Step2: Reverse - translate $B'$

If the translation rule is $(x,y)\to(x + 1,y - 3)$, to find the pre - image of $B'(-1,0)$, we solve the following equations for the coordinates of $B(x_0,y_0)$: $x_0+1=-1$ and $y_0-3 = 0$.
For the $x$-coordinate of $B$: $x_0=-1 - 1=-2$.
For the $y$-coordinate of $B$: $y_0=0 + 3=3$.

Answer:

$B(-2,3)$