Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 18E
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Question
![### Distance Between Points in a Coordinate Plane
To calculate the distance between two points in a coordinate plane, you can use the Distance Formula:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here are a couple of examples:
**2) What is the distance between points (-1, 3) and (5, -2)?**
Using the Distance Formula:
\[ x_1 = -1, \; y_1 = 3, \; x_2 = 5, \; y_2 = -2 \]
\[ \text{Distance} = \sqrt{(5 - (-1))^2 + (-2 - 3)^2} \]
\[ \text{Distance} = \sqrt{(5 + 1)^2 + (-2 - 3)^2} \]
\[ \text{Distance} = \sqrt{6^2 + (-5)^2} \]
\[ \text{Distance} = \sqrt{36 + 25} \]
\[ \text{Distance} = \sqrt{61} \]
\[ \text{Distance} = 7.81 \]
Hence, the distance between the points (-1, 3) and (5, -2) is approximately 7.81 units.
---
**3) What is the distance between points (0, -1) and (10, -5)?**
Using the Distance Formula:
\[ x_1 = 0, \; y_1 = -1, \; x_2 = 10, \; y_2 = -5 \]
\[ \text{Distance} = \sqrt{(10 - 0)^2 + (-5 - (-1))^2} \]
\[ \text{Distance} = \sqrt{10^2 + (-5 + 1)^2} \]
\[ \text{Distance} = \sqrt{10^2 + (-4)^2} \]
\[ \text{Distance} = \sqrt{100 + 16} \]
\[ \text{Distance} = \sqrt{116} \]
\[ \text{Distance} = 10.77 \]
Hence, the distance between the points (0, -1) and (10, -5) is approximately 10.77 units.
These examples demonstrate how to apply](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3829f931-9257-40ee-99af-de1dd428439e%2F316ecc0f-a60d-47a8-be48-c3d9e2781dfd%2Fr72jcmr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Distance Between Points in a Coordinate Plane
To calculate the distance between two points in a coordinate plane, you can use the Distance Formula:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here are a couple of examples:
**2) What is the distance between points (-1, 3) and (5, -2)?**
Using the Distance Formula:
\[ x_1 = -1, \; y_1 = 3, \; x_2 = 5, \; y_2 = -2 \]
\[ \text{Distance} = \sqrt{(5 - (-1))^2 + (-2 - 3)^2} \]
\[ \text{Distance} = \sqrt{(5 + 1)^2 + (-2 - 3)^2} \]
\[ \text{Distance} = \sqrt{6^2 + (-5)^2} \]
\[ \text{Distance} = \sqrt{36 + 25} \]
\[ \text{Distance} = \sqrt{61} \]
\[ \text{Distance} = 7.81 \]
Hence, the distance between the points (-1, 3) and (5, -2) is approximately 7.81 units.
---
**3) What is the distance between points (0, -1) and (10, -5)?**
Using the Distance Formula:
\[ x_1 = 0, \; y_1 = -1, \; x_2 = 10, \; y_2 = -5 \]
\[ \text{Distance} = \sqrt{(10 - 0)^2 + (-5 - (-1))^2} \]
\[ \text{Distance} = \sqrt{10^2 + (-5 + 1)^2} \]
\[ \text{Distance} = \sqrt{10^2 + (-4)^2} \]
\[ \text{Distance} = \sqrt{100 + 16} \]
\[ \text{Distance} = \sqrt{116} \]
\[ \text{Distance} = 10.77 \]
Hence, the distance between the points (0, -1) and (10, -5) is approximately 10.77 units.
These examples demonstrate how to apply
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