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
Related questions
Question
![**Question:**
6) Find the length of the segment. Round to the nearest tenth of a unit.
**Graph Explanation:**
Below the question, there is a coordinate plane diagram showing points G, H, and J with the following coordinates:
- Point \( G(-2, 4) \)
- Point \( H(5, 5) \)
- Point \( J(4, -1) \)
The coordinate plane is labeled with x and y axes, and the grid has markings for each unit.
To find the length of the segment connecting any two points, we use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
**Example Calculation:**
If we need to find the distance between points G and H:
\[ x_1 = -2, \, y_1 = 4 \, \text{(for point G)} \]
\[ x_2 = 5, \, y_2 = 5 \, \text{(for point H)} \]
Using the distance formula:
\[ d = \sqrt{(5 - (-2))^2 + (5 - 4)^2} \]
\[ d = \sqrt{(5 + 2)^2 + 1^2} \]
\[ d = \sqrt{7^2 + 1^2} \]
\[ d = \sqrt{49 + 1} \]
\[ d = \sqrt{50} \]
\[ d \approx 7.1 \, \text{units (rounded to the nearest tenth)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1443ecf-7a36-4d10-b843-bbaa3b340a11%2Fd23109ec-8fca-4275-a569-cbe3d2574ec7%2Fiih6sdn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
6) Find the length of the segment. Round to the nearest tenth of a unit.
**Graph Explanation:**
Below the question, there is a coordinate plane diagram showing points G, H, and J with the following coordinates:
- Point \( G(-2, 4) \)
- Point \( H(5, 5) \)
- Point \( J(4, -1) \)
The coordinate plane is labeled with x and y axes, and the grid has markings for each unit.
To find the length of the segment connecting any two points, we use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
**Example Calculation:**
If we need to find the distance between points G and H:
\[ x_1 = -2, \, y_1 = 4 \, \text{(for point G)} \]
\[ x_2 = 5, \, y_2 = 5 \, \text{(for point H)} \]
Using the distance formula:
\[ d = \sqrt{(5 - (-2))^2 + (5 - 4)^2} \]
\[ d = \sqrt{(5 + 2)^2 + 1^2} \]
\[ d = \sqrt{7^2 + 1^2} \]
\[ d = \sqrt{49 + 1} \]
\[ d = \sqrt{50} \]
\[ d \approx 7.1 \, \text{units (rounded to the nearest tenth)} \]
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