Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Topic Video
Question
Can you help me figure this problem out.
**Graph Explanation:**
- The graph is a standard (x, y) coordinate grid ranging from -10 to +10 on both axes.
- The origin (0, 0) is marked at the intersection of the x-axis and y-axis.
- Three points are marked as A, B, and C:
- Point A is located at the origin (0,0).
- Vector AB extends from A to B. B is positioned at (2, 4) on the graph.
- Vector AC extends from A to C. C is positioned at (4, 0) on the graph.
**Vector Addition:**
To find the ordered pair that represents the vector addition \(\bar{AB}\) + \(\bar{AC}\):
- The coordinates of B are (2, 4), which means \(\bar{AB}\) can be represented as \(\langle 2, 4 \rangle\).
- The coordinates of C are (4, 0), which means \(\bar{AC}\) can be represented as \(\langle 4, 0 \rangle\).
**Adding Vectors:**
To add vectors \(\langle 2, 4 \rangle\) and \(\langle 4, 0 \rangle\):
- Add the x-coordinates: 2 + 4 = 6
- Add the y-coordinates: 4 + 0 = 4
Therefore, \(\bar{AB}\) + \(\bar{AC}\) results in the ordered pair (6, 4).
**Question:**
What is the ordered pair that represents \(\bar{AB}\) + \(\bar{AC}\)?
**Answer:**
The ordered pair is ( __ , __ ).
**Solution:**
The ordered pair is (6 , 4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa19b2cf3-e4ba-4c54-87ea-4b78f08e1dba%2F1739530e-a9c6-4b85-afbd-733b870f2efd%2F224dtbe_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Vectors Addition through Graphs**
Two vectors are graphed below on a Cartesian coordinate plane.
**Graph Explanation:**
- The graph is a standard (x, y) coordinate grid ranging from -10 to +10 on both axes.
- The origin (0, 0) is marked at the intersection of the x-axis and y-axis.
- Three points are marked as A, B, and C:
- Point A is located at the origin (0,0).
- Vector AB extends from A to B. B is positioned at (2, 4) on the graph.
- Vector AC extends from A to C. C is positioned at (4, 0) on the graph.
**Vector Addition:**
To find the ordered pair that represents the vector addition \(\bar{AB}\) + \(\bar{AC}\):
- The coordinates of B are (2, 4), which means \(\bar{AB}\) can be represented as \(\langle 2, 4 \rangle\).
- The coordinates of C are (4, 0), which means \(\bar{AC}\) can be represented as \(\langle 4, 0 \rangle\).
**Adding Vectors:**
To add vectors \(\langle 2, 4 \rangle\) and \(\langle 4, 0 \rangle\):
- Add the x-coordinates: 2 + 4 = 6
- Add the y-coordinates: 4 + 0 = 4
Therefore, \(\bar{AB}\) + \(\bar{AC}\) results in the ordered pair (6, 4).
**Question:**
What is the ordered pair that represents \(\bar{AB}\) + \(\bar{AC}\)?
**Answer:**
The ordered pair is ( __ , __ ).
**Solution:**
The ordered pair is (6 , 4).
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