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
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![**Question:**
Find the distance between the two points *
[Insert image showing a graph with two points plotted and a right triangle illustrated]
The graph depicts a Cartesian coordinate system with the x-axis labeled from -4 to 4 and the y-axis labeled similarly.
Two points are marked on the graph:
- The first point is at (0, 2)
- The second point is at (4, -2)
These points are connected by a straight line, and a right triangle is formed by drawing a horizontal line from (0, 2) to (4, 2) and a vertical line from (4, 2) to (4, -2).
The length of the horizontal leg of the triangle measures 4 units, and the length of the vertical leg measures 4 units.
Using the Pythagorean theorem to find the distance between the two points:
\[ \text{Distance} = \sqrt{(4 - 0)^2 + (2 - (-2))^2} \]
\[ = \sqrt{4^2 + 4^2} \]
\[ = \sqrt{16 + 16} \]
\[ = \sqrt{32} \]
\[ = 4\sqrt{2} \]
**Answer Choices:**
A) \( 2\sqrt{5} \)
B) \( 2\sqrt{10} \)
C) \( 2\sqrt{2} \)
D) \( 4\sqrt{2} \)
The correct answer is: **D) \( 4\sqrt{2} \)**
---
**Explanation of Diagram:**
The diagram is a graph showing two points and a right triangle whose hypotenuse is the line segment connecting the two points. The horizontal and vertical distances are labeled, showing 4 units each. By calculating the hypotenuse using the Pythagorean theorem, the distance between the two points is determined to be \( 4\sqrt{2} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb294f3d7-c37e-4d19-872e-5bb2e2baac27%2F26333dc7-cb8f-48e5-a62a-746d1371c8a6%2Fxo046zt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Find the distance between the two points *
[Insert image showing a graph with two points plotted and a right triangle illustrated]
The graph depicts a Cartesian coordinate system with the x-axis labeled from -4 to 4 and the y-axis labeled similarly.
Two points are marked on the graph:
- The first point is at (0, 2)
- The second point is at (4, -2)
These points are connected by a straight line, and a right triangle is formed by drawing a horizontal line from (0, 2) to (4, 2) and a vertical line from (4, 2) to (4, -2).
The length of the horizontal leg of the triangle measures 4 units, and the length of the vertical leg measures 4 units.
Using the Pythagorean theorem to find the distance between the two points:
\[ \text{Distance} = \sqrt{(4 - 0)^2 + (2 - (-2))^2} \]
\[ = \sqrt{4^2 + 4^2} \]
\[ = \sqrt{16 + 16} \]
\[ = \sqrt{32} \]
\[ = 4\sqrt{2} \]
**Answer Choices:**
A) \( 2\sqrt{5} \)
B) \( 2\sqrt{10} \)
C) \( 2\sqrt{2} \)
D) \( 4\sqrt{2} \)
The correct answer is: **D) \( 4\sqrt{2} \)**
---
**Explanation of Diagram:**
The diagram is a graph showing two points and a right triangle whose hypotenuse is the line segment connecting the two points. The horizontal and vertical distances are labeled, showing 4 units each. By calculating the hypotenuse using the Pythagorean theorem, the distance between the two points is determined to be \( 4\sqrt{2} \).
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