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 translation vector

The translation from $A(5,1)$ to $A'(6, - 2)$ means for the $x$-coordinate, the change is $\Delta x=6 - 5=1$, and for the $y$-coordinate, the change is $\Delta y=-2 - 1=-3$.

Step2: Reverse - translate $B'$

Let the coordinates of $B$ be $(x,y)$. We know that to get from $B$ to $B'$ we apply the same translation. So if $B'(-1,0)$ and the translation is $(1,-3)$, then for the $x$-coordinate of $B$, $x=-1 - 1=-2$, and for the $y$-coordinate of $B$, $y=0+3 = 3$.

Answer:

$(-2,3)$