We have been given that in the coordinate plane, the point A(2, -1) is translated to the point A’(3, 2). We are asked to find the coordinates of point B' and C' under the same translation.
First of all, we will find the transformation rule from A to A'.
We can see that x-coordinate of point A' is 1 more than x-coordinate of A.
So transformation rule for x-coordinate would be [tex]x\rightarrow (x+1)[/tex].
We can also see that y-coordinate of A' is 3 more than y-coordinate of A.
So transformation rule for y-coordinate would be [tex]y\rightarrow (y+3)[/tex].
Now we will use these rules to find B' and C' from B(6,1) and C[tex](4,-4)[/tex].
[tex]B'=(6+1,1+3)=(7,4)[/tex]
[tex]C'=(4+1,-4+3)=(5,-1)[/tex]
Therefore, the coordinates of B' and C' are [tex](7,4)[/tex] and [tex](5,-1)[/tex] respectively.
