Question

Use the image to answer the question.

A rectangle is labeled upper A upper B upper C upper D. Vertices upper A and upper B are labeled as follows: upper A equals left parenthesis negative 5 comma 4 right parenthesis, and upper B equals left parenthesis negative 1 comma 4 right parenthesis.

After applying a translation vector to rectangle ABDC , the coordinates of A′ are (−6,8) . What are the coordinates of B′ ?

(1 point)
(,)

Answer 1

To find the coordinates of \( B' \), we first need to determine the translation vector applied to rectangle \( ABCD \).

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

To find the translation vector, we can calculate the difference in the x-coordinates and y-coordinates:

\[
\text{Translation in x} = -6 - (-5) = -6 + 5 = -1
\]
\[
\text{Translation in y} = 8 - 4 = 4
\]

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

Now, we need the original coordinates of point \( B \). The coordinates of point \( B \) are given as \( B(-1, 4) \).

We will apply the translation vector \( (-1, 4) \) to the coordinates of \( B \):

\[
B' = B + \text{Translation vector}
\]
\[
B' = (-1, 4) + (-1, 4) = (-1 - 1, 4 + 4) = (-2, 8)
\]

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

Therefore, the answer is:

\[
(-2, 8)
\]