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

Question

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Answer 1

To find the coordinates of B' after translation, we first determine the translation vector applied to the rectangle.

Given that the coordinates of A are A(-3, 2) and A' are A'(-6, 8), we can find the translation vector \( T \) as follows:

\[ T = (x_{A'} - x_A, y_{A'} - y_A) \] \[ T = (-6 - (-3), 8 - 2) = (-6 + 3, 8 - 2) = (-3, 6) \]

Now, we apply this translation vector \( T \) to the point B(1, 2) to find the coordinates of B':

\[ B' = (x_B + T_x, y_B + T_y) \] \[ B' = (1 + (-3), 2 + 6) = (1 - 3, 2 + 6) = (-2, 8) \]

Thus, the coordinates of B' are:

\[ \boxed{(-2, 8)} \]