Question

A = (-5,4) B = (-1,4)

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

Answer 1

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

The original coordinates of point A are \( A = (-5, 4) \), and the new coordinates after translation are \( A' = (-6, 8) \).

The translation vector \( T \) can be calculated as follows:

\[
T_x = A'_x - A_x = -6 - (-5) = -6 + 5 = -1
\]

\[
T_y = A'_y - A_y = 8 - 4 = 4
\]

Thus, the translation vector is \( T = (-1, 4) \).

Now, we apply this translation vector to point B:

The original coordinates of point B are \( B = (-1, 4) \).

Calculating the new coordinates \( B' \):

\[
B'_x = B_x + T_x = -1 + (-1) = -1 - 1 = -2
\]

\[
B'_y = B_y + T_y = 4 + 4 = 8
\]

So, the coordinates of \( B' \) after the translation are \( B' = (-2, 8) \).