Question

Two vectors drawn.Two vectors are drawn on a coordinate plane. Vector v has an initial point left-parenthesis negative 2 comma 3 right-parenthesis and terminal point left-parenthesis 4 comma 4 right-parenthesis. Vector u has an initial point left-parenthesis 4 comma negative 2 right-parenthesis and terminal point left-parenthesis 5 comma 3 right-parenthesis.
Question
Use the image to answer the question.
Find u + v.
(1 point)
Responses

u + v = 12
u + v = 12

bold u plus bold v equals left angle bracket 7 comma 6 right angle bracket
Image with alt text: bold u plus bold v equals left angle bracket 7 comma 6 right angle bracket

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

bold u plus bold v equals negative 12
Image with alt text: bold u plus bold v equals negative 12
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Answer 1

To find the sum of vectors \( \mathbf{u} \) and \( \mathbf{v} \), we need to first determine their components.

1. **Calculate the components of vector \( \mathbf{v} \)**:
- Initial point: \( (-2, 3) \)
- Terminal point: \( (4, 4) \)
- The components of vector \( \mathbf{v} \) are calculated as follows:
\[
\mathbf{v} = (4 - (-2), 4 - 3) = (4 + 2, 4 - 3) = (6, 1)
\]

2. **Calculate the components of vector \( \mathbf{u} \)**:
- Initial point: \( (4, -2) \)
- Terminal point: \( (5, 3) \)
- The components of vector \( \mathbf{u} \) are calculated as follows:
\[
\mathbf{u} = (5 - 4, 3 - (-2)) = (1, 3 + 2) = (1, 5)
\]

3. **Calculate \( \mathbf{u} + \mathbf{v} \)**:
\[
\mathbf{u} + \mathbf{v} = (1, 5) + (6, 1) = (1 + 6, 5 + 1) = (7, 6)
\]

Thus, the result of \( \mathbf{u} + \mathbf{v} \) is:
\[
\mathbf{u} + \mathbf{v} = \langle 7, 6 \rangle
\]

Based on the responses provided, the correct answer is:
**bold u plus bold v equals left angle bracket 7 comma 6 right angle bracket**.