Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
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### Length of Line Segments in Coordinate Geometry
#### Problem:
Use the figure shown to find the length of each segment.
#### Figure Explanation:
The diagram provided is a number line with three points labeled G, H, and I:
- Point G is located at -5 on the number line.
- Point H is located at 12 on the number line.
- Point I is located at 21 on the number line.
#### Objective:
Calculate the lengths of the segments GH, HI, and GI using the coordinates provided.
#### Calculations:
**1. Length of GH:**
\[ GH = |H - G| = |12 - (-5)| = |12 + 5| = 17 \]
**2. Length of HI:**
\[ HI = |I - H| = |21 - 12| = 9 \]
**3. Length of GI:**
\[ GI = |I - G| = |21 - (-5)| = |21 + 5| = 26 \]
---
#### Solution Template:
Please input the calculated values in the blanks provided below:
- GH = **17**
- HI = **9**
- GI = **26**
---
This example illustrates how to find the distances between points on a number line using absolute values of their coordinates. This fundamental approach is crucial for understanding more complex topics in coordinate geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6f562ff-b630-4ff7-a4a4-0cf52896afb3%2F78cabb10-08b9-4481-93f2-b0775c7cb604%2Fxknl66e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Length of Line Segments in Coordinate Geometry
#### Problem:
Use the figure shown to find the length of each segment.
#### Figure Explanation:
The diagram provided is a number line with three points labeled G, H, and I:
- Point G is located at -5 on the number line.
- Point H is located at 12 on the number line.
- Point I is located at 21 on the number line.
#### Objective:
Calculate the lengths of the segments GH, HI, and GI using the coordinates provided.
#### Calculations:
**1. Length of GH:**
\[ GH = |H - G| = |12 - (-5)| = |12 + 5| = 17 \]
**2. Length of HI:**
\[ HI = |I - H| = |21 - 12| = 9 \]
**3. Length of GI:**
\[ GI = |I - G| = |21 - (-5)| = |21 + 5| = 26 \]
---
#### Solution Template:
Please input the calculated values in the blanks provided below:
- GH = **17**
- HI = **9**
- GI = **26**
---
This example illustrates how to find the distances between points on a number line using absolute values of their coordinates. This fundamental approach is crucial for understanding more complex topics in coordinate geometry.
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