Question

After applying a translation vector to rectangle ABCD, the coordinates of A' are (-6,8). What are the coordinates of B'?
(The original coordinates of A and B are A(-5,4) and B(-1,4))
A. (3,8)
B. (-1,6)
C. (-2,8)
D. (2,4)

Answer 1

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

The coordinates of point A and its translated version A' are given as:
- Original point A: (-5, 4)
- Translated point A': (-6, 8)

To find the translation vector \( \vec{t} \), we calculate the differences in the x and y coordinates:
- For the x-coordinate: \( -6 - (-5) = -1 \)
- For the y-coordinate: \( 8 - 4 = 4 \)

Thus, the translation vector \( \vec{t} \) is \( (-1, 4) \).

Now, we apply this same translation to point B. The original coordinates of B are:
- B: (-1, 4)

Applying the translation vector \( \vec{t} \) to B:
- For the x-coordinate of B':
\[
-1 + (-1) = -2
\]
- For the y-coordinate of B':
\[
4 + 4 = 8
\]

So, the coordinates of B' are:
\[
B' = (-2, 8)
\]

Therefore, the correct answer is:
C. (-2, 8)