The coordinates of B before translated to B' are (-2,3).
Translation is a term used in geometry to describe a function that moves an object a certain distance. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
For the given situation,
Triangle ABC is translated to image A’B’C’.
In this translation, A(5, 1) maps to A’(6,-2).
In translation, the distance between A' and A in the coordinate system is same as B'B and C'C.
Let A(x1,y1) = (5,1) and A'(x2,y2) = (6,-2)
⇒ [tex]x1-x2 = 5-6[/tex]
⇒ [tex]-1[/tex]
⇒ [tex]y1-y2=1-(-2)[/tex]
⇒ [tex]3[/tex]
The coordinates of B’(-1,0)
So, the coordinates of B is
⇒ [tex]x=(-1-1)=-2[/tex]
⇒ [tex]y=(0+3)=3[/tex]
Thus coordinates of B are (-2,3).
Hence we can conclude that the coordinates of B before translation are (-2,3).
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