Use the image to answer the question.

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 \( B' \) after the translation, we first need to determine the translation vector used to move point \( A \) to point \( A' \).

The coordinates of point \( A \) are \( (-5, 4) \), and the coordinates of point \( A' \) are \( (-6, 8) \).

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

1. Change in x (\(\Delta x\)): \[ \Delta x = -6 - (-5) = -6 + 5 = -1 \]

2. Change in y (\(\Delta y\)): \[ \Delta y = 8 - 4 = 4 \]

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

Now, we apply this translation vector to point \( B \), which has the coordinates \( (-1, 4) \).

Calculate \( B' \) using the same translation:

1. New x-coordinate of \( B' \): \[ x' = -1 + (-1) = -2 \]

2. New y-coordinate of \( B' \): \[ y' = 4 + 4 = 8 \]

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

So, the final answer is:

\[ (-2, 8) \]