Answer: (-2, 3)
Step-by-step explanation:
A translation is when all the points of an image are moved by a certain distance horizontally and a certain distance vertically. If we can find the exact rule of translation from point A and A' (A prime, the point A after the translation), then we can do the reverse to B' to get the coordinate for B.
We can find how A turns into A' by essentially doing A' - A.
[tex]x: 6 - 5 = 1\\y: -2 - 1= -3[/tex]
Now we know that the translation rule is to move the image 1 unit to the right and 3 units down. Let's apply the reverse of this translation to B'.
B' will turn into B by doing the reverse of the translation: moving the image 1 unit to the left and 3 units up. Let's apply this:
[tex]x: -1 - 1 = -2\\y: 0 + 3 = 3[/tex]
The coordinates of B are (-2,3).