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
![**Example 3: Distance Between Two Points**
**Problem:**
What is the approximate length of \(RS\) with endpoints \(R(2, 3)\) and \(S(4, -1)\)?
- A) 1.4 units
- B) 4.0 units
- C) 4.5 units
- D) 6 units
**Solution:**
Use the Distance Formula. You may find it helpful to draw a diagram.
\[RS = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
\[= \sqrt{(4 - 2)^2 + ((-1) - 3)^2}\]
\[= \sqrt{(2)^2 + (-4)^2}\]
\[= \sqrt{4 + 16}\]
\[= \sqrt{20}\]
\[≈ 4.47\]
**The correct answer is C.**
**Guided Practice for Example #3**
4. In Example 3, does it matter which ordered pair you choose to substitute for \((x_1, y_1)\) and which ordered pair you choose to substitute for \((x_2, y_2)\)? Explain.
5. What is the approximate length of segment \(AB\), with endpoints \(A (-3, 2)\) and \(B (1, -4)\)?
**Diagram:**
There is a graph in the solution that provides a visual representation of the points \(R(2, 3)\) and \(S(4, -1)\) on a coordinate plane. The points are connected by a straight diagonal line that illustrates the distance between them. The x-axis and y-axis are both labeled with numbers for reference.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3829f931-9257-40ee-99af-de1dd428439e%2Faeaedbf7-bdad-4e2e-ad45-9913330e1a07%2Fj937ibq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example 3: Distance Between Two Points**
**Problem:**
What is the approximate length of \(RS\) with endpoints \(R(2, 3)\) and \(S(4, -1)\)?
- A) 1.4 units
- B) 4.0 units
- C) 4.5 units
- D) 6 units
**Solution:**
Use the Distance Formula. You may find it helpful to draw a diagram.
\[RS = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
\[= \sqrt{(4 - 2)^2 + ((-1) - 3)^2}\]
\[= \sqrt{(2)^2 + (-4)^2}\]
\[= \sqrt{4 + 16}\]
\[= \sqrt{20}\]
\[≈ 4.47\]
**The correct answer is C.**
**Guided Practice for Example #3**
4. In Example 3, does it matter which ordered pair you choose to substitute for \((x_1, y_1)\) and which ordered pair you choose to substitute for \((x_2, y_2)\)? Explain.
5. What is the approximate length of segment \(AB\), with endpoints \(A (-3, 2)\) and \(B (1, -4)\)?
**Diagram:**
There is a graph in the solution that provides a visual representation of the points \(R(2, 3)\) and \(S(4, -1)\) on a coordinate plane. The points are connected by a straight diagonal line that illustrates the distance between them. The x-axis and y-axis are both labeled with numbers for reference.
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 3 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