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
![### Finding the Length of Line Segment AB
To determine the length of line segment \( AB \) to the nearest hundredth, follow these steps:
1. **Identify the Coordinates:**
- Point \( A \) has coordinates (-3, -3).
- Point \( B \) has coordinates (2, 3).
2. **Apply the Distance Formula:**
The distance formula is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
3. **Substitute the Coordinates into the Formula:**
- \( x_1 = -3 \)
- \( y_1 = -3 \)
- \( x_2 = 2 \)
- \( y_2 = 3 \)
Now substitute:
\[ d = \sqrt{(2 - (-3))^2 + (3 - (-3))^2} \]
Simplify inside the parentheses:
\[ d = \sqrt{(2 + 3)^2 + (3 + 3)^2} \]
\[ d = \sqrt{5^2 + 6^2} \]
\[ d = \sqrt{25 + 36} \]
\[ d = \sqrt{61} \]
4. **Calculate the Distance:**
\[ d \approx 7.81 \]
Therefore, the length of \( AB \) is approximately \( 7.81 \).
### Description of the Diagram
The diagram displays a Cartesian coordinate plane with \( x \)- and \( y \)-axes labeled and grid lines marked at intervals. Two points are plotted:
- Point \( A \) at coordinates (-3, -3)
- Point \( B \) at coordinates (2, 3)
There is a line segment connecting Points \( A \) and \( B \). The goal is to determine the length of this line segment using the distance formula.
The text box below the diagram is intended to record the calculated length of line segment \( AB \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c4efd14-ad12-4da1-952e-6336419295ab%2F2031cc79-3087-4d06-85ed-8320ff8af0a3%2F0raqpln_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Length of Line Segment AB
To determine the length of line segment \( AB \) to the nearest hundredth, follow these steps:
1. **Identify the Coordinates:**
- Point \( A \) has coordinates (-3, -3).
- Point \( B \) has coordinates (2, 3).
2. **Apply the Distance Formula:**
The distance formula is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
3. **Substitute the Coordinates into the Formula:**
- \( x_1 = -3 \)
- \( y_1 = -3 \)
- \( x_2 = 2 \)
- \( y_2 = 3 \)
Now substitute:
\[ d = \sqrt{(2 - (-3))^2 + (3 - (-3))^2} \]
Simplify inside the parentheses:
\[ d = \sqrt{(2 + 3)^2 + (3 + 3)^2} \]
\[ d = \sqrt{5^2 + 6^2} \]
\[ d = \sqrt{25 + 36} \]
\[ d = \sqrt{61} \]
4. **Calculate the Distance:**
\[ d \approx 7.81 \]
Therefore, the length of \( AB \) is approximately \( 7.81 \).
### Description of the Diagram
The diagram displays a Cartesian coordinate plane with \( x \)- and \( y \)-axes labeled and grid lines marked at intervals. Two points are plotted:
- Point \( A \) at coordinates (-3, -3)
- Point \( B \) at coordinates (2, 3)
There is a line segment connecting Points \( A \) and \( B \). The goal is to determine the length of this line segment using the distance formula.
The text box below the diagram is intended to record the calculated length of line segment \( AB \).
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