After applying a translation vector to rectangle ABCD, the coordinates A = (-3,2) B =(1,2) the coordinates of A' are (-6,8). What are the coordinates of B'?

Answer 1

To find the coordinates of point B' after the same translation that applied to point A to get from A to A', we first need to determine the translation vector.

The translation can be found by determining the difference in the coordinates of A and A':

\[ A' = A + T \] where \( T \) is the translation vector. Rearranging gives us:

\[ T = A' - A \]

Now, substituting the coordinates of point A and A':

\[ T = (-6, 8) - (-3, 2) = (-6 + 3, 8 - 2) = (-3, 6) \]

Now that we have the translation vector \( T = (-3, 6) \), we can apply this same translation to point B.

The coordinates of point B are \( (1, 2) \), so we calculate B' as follows:

\[ B' = B + T = (1, 2) + (-3, 6) = (1 - 3, 2 + 6) = (-2, 8) \]

Therefore, the coordinates of B' are \((-2, 8)\).