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
![### Problem 3: Finding the Length of a Segment
**Question:**
Find the length of the segment. Round to the nearest tenth of a unit.
**Diagram:**
The diagram provided is a coordinate plane with two points marked:
- Point S is located at (-1, 2).
- Point T is located at (3, -2).
A line segment connects points S and T.
### Explanation:
To find the length of the segment ST, we use the distance formula for two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For points \((x_1, y_1) = (-1, 2)\) and \((x_2, y_2) = (3, -2)\):
1. Substitute the coordinates into the distance formula:
\[ \text{Distance} = \sqrt{(3 - (-1))^2 + (-2 - 2)^2} \]
2. Simplify the expressions inside the square root:
\[ \text{Distance} = \sqrt{(3 + 1)^2 + (-2 - 2)^2} \]
\[ \text{Distance} = \sqrt{(4)^2 + (-4)^2} \]
3. Calculate the squares:
\[ \text{Distance} = \sqrt{16 + 16} \]
\[ \text{Distance} = \sqrt{32} \]
4. Simplify the square root:
\[ \text{Distance} = \sqrt{32} \approx 5.7 \]
### Conclusion:
The length of the segment ST, rounded to the nearest tenth, is approximately **5.7 units**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae7e7cf3-425c-45db-adb3-f49e9589ee4b%2F5f4cc456-aede-4c6f-a555-c58b087d7b5c%2Firar3cg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 3: Finding the Length of a Segment
**Question:**
Find the length of the segment. Round to the nearest tenth of a unit.
**Diagram:**
The diagram provided is a coordinate plane with two points marked:
- Point S is located at (-1, 2).
- Point T is located at (3, -2).
A line segment connects points S and T.
### Explanation:
To find the length of the segment ST, we use the distance formula for two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For points \((x_1, y_1) = (-1, 2)\) and \((x_2, y_2) = (3, -2)\):
1. Substitute the coordinates into the distance formula:
\[ \text{Distance} = \sqrt{(3 - (-1))^2 + (-2 - 2)^2} \]
2. Simplify the expressions inside the square root:
\[ \text{Distance} = \sqrt{(3 + 1)^2 + (-2 - 2)^2} \]
\[ \text{Distance} = \sqrt{(4)^2 + (-4)^2} \]
3. Calculate the squares:
\[ \text{Distance} = \sqrt{16 + 16} \]
\[ \text{Distance} = \sqrt{32} \]
4. Simplify the square root:
\[ \text{Distance} = \sqrt{32} \approx 5.7 \]
### Conclusion:
The length of the segment ST, rounded to the nearest tenth, is approximately **5.7 units**.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning