Answer:
The coordinates of B' and C' are [tex]B'(x,y) = (4,4)[/tex] and [tex]C'(x,y) = (8, -1)[/tex].
Step-by-step explanation:
Vectorially speaking, the translation of a point is represented by the following operation:
[tex]P'(x,y) = P(x,y) + T(x,y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.
[tex]P'(x,y)[/tex] - Translated point.
[tex]T(x,y)[/tex] - Translation vector.
First, we need to calculate the translation vector after knowing that [tex]A(x,y) = (3,4)[/tex] and [tex]A'(x,y) = (6,2)[/tex]. That is:
[tex]T(x,y) = A'(x,y) - A(x,y)[/tex]
[tex]T(x,y) = (6,2) - (3,4)[/tex]
[tex]T(x,y) = (3, -2)[/tex]
Finally, we determine the coordinates of points B' and C':
[tex]B(x,y) = (1,6)[/tex], [tex]T(x,y) = (3, -2)[/tex]
[tex]B'(x,y) = (1,6) + (3,-2)[/tex]
[tex]B'(x,y) = (4,4)[/tex]
[tex]C(x,y) = (5,1)[/tex], [tex]T(x,y) = (3, -2)[/tex]
[tex]C'(x,y) = (5,1) + (3,-2)[/tex]
[tex]C'(x,y) = (8, -1)[/tex]
The coordinates of B' and C' are [tex]B'(x,y) = (4,4)[/tex] and [tex]C'(x,y) = (8, -1)[/tex].
