Question

Vector v is drawn on a coordinate plane. It goes from A left-parenthesis 1 comma 3 right-parenthesis to B left-parenthesis 7 comma 1 right-parenthesis.
Question
Use the image to answer the question.
Find the component form of vector v that has an initial point at A and a terminal point at B.
(1 point)
Responses

bold v equals left angle bracket 8 comma 4 right angle bracket
Image with alt text: bold v equals left angle bracket 8 comma 4 right angle bracket

bold v equals left angle bracket 6 comma negative 2 right angle bracket
Image with alt text: bold v equals left angle bracket 6 comma negative 2 right angle bracket

bold v equals left angle bracket negative 6 comma 2 right angle bracket
Image with alt text: bold v equals left angle bracket negative 6 comma 2 right angle bracket

bold v equals left angle bracket 4 comma 0 right angle bracket
Image with alt text: bold v equals left angle bracket 4 comma 0 right angle bracket
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Answer 1

To find the component form of vector \( \mathbf{v} \) that goes from point \( A(1, 3) \) to point \( B(7, 1) \), we use the formula:

\[
\mathbf{v} = \langle x_2 - x_1, y_2 - y_1 \rangle
\]

where \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \).

Plugging in the coordinates:

\[
\mathbf{v} = \langle 7 - 1, 1 - 3 \rangle = \langle 6, -2 \rangle
\]

So the component form of vector \( \mathbf{v} \) is:

\[
\mathbf{v} = \langle 6, -2 \rangle
\]

Thus, the correct response is:

**bold v equals left angle bracket 6 comma negative 2 right angle bracket**