Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Example Problem:**
**Suppose** \( A = (-8, 7) \) **and** \( \overrightarrow{AB} = \langle 4, -3 \rangle \). **Then**
\[ B = \ __ \ ]
**Help:** (Points)
---
**Detailed Explanation:**
To find the coordinates of point \( B \), we will use the information given about point \( A \) and the vector \( \overrightarrow{AB} \).
The vector \( \overrightarrow{AB} \) tells us how to get from point \( A \) to point \( B \). Specifically, the vector \( \langle 4, -3 \rangle \) indicates that from point \( A \), we move 4 units in the positive x-direction and 3 units in the negative y-direction to reach point \( B \).
Given:
\[ A = (-8, 7) \]
\[ \overrightarrow{AB} = \langle 4, -3 \rangle \]
So, to find \( B \):
1. Add the x-component of the vector to the x-coordinate of point \( A \):
\[ x_B = -8 + 4 = -4 \]
2. Add the y-component of the vector to the y-coordinate of point \( A \):
\[ y_B = 7 + (-3) = 4 \]
Thus, the coordinates of point \( B \) are:
\[ B = (-4, 4) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa77ad668-7ef6-46eb-bde1-e7c4f652c232%2F1603b4f1-7a36-4872-a2bd-6c19a03d8e44%2Fpyuw12_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem:**
**Suppose** \( A = (-8, 7) \) **and** \( \overrightarrow{AB} = \langle 4, -3 \rangle \). **Then**
\[ B = \ __ \ ]
**Help:** (Points)
---
**Detailed Explanation:**
To find the coordinates of point \( B \), we will use the information given about point \( A \) and the vector \( \overrightarrow{AB} \).
The vector \( \overrightarrow{AB} \) tells us how to get from point \( A \) to point \( B \). Specifically, the vector \( \langle 4, -3 \rangle \) indicates that from point \( A \), we move 4 units in the positive x-direction and 3 units in the negative y-direction to reach point \( B \).
Given:
\[ A = (-8, 7) \]
\[ \overrightarrow{AB} = \langle 4, -3 \rangle \]
So, to find \( B \):
1. Add the x-component of the vector to the x-coordinate of point \( A \):
\[ x_B = -8 + 4 = -4 \]
2. Add the y-component of the vector to the y-coordinate of point \( A \):
\[ y_B = 7 + (-3) = 4 \]
Thus, the coordinates of point \( B \) are:
\[ B = (-4, 4) \]
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