Understanding the calculation of the length of a line segment in coordinate geometry is vital. This knowledge enables us to find the distance between two points on a Cartesian plane, a fundamental concept in many mathematical and real-world applications.
Introduction to the Distance Formula
The distance between any two points and on a Cartesian plane is calculated using the distance formula, which is an application of Pythagoras' theorem:
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Calculating the Length of a Line Segment
Example 1: Basic Calculation
Find the length of the line segment between and .
Solution:
1. Identify Coordinates:
, , , .
2. Apply the Formula:
The length of the line segment AB is 5 units.
Example 2: Negative Coordinates
Calculate the length of the line segment between and .
Solution:
1. Coordinates:
2. Apply the Formula:
The length of CD is units.
Practice Problems
Problem 1
Find the length of the line segment between and .
Solution:
1. Coordinates:
2. Apply the Formula:
Problem 2
Calculate the distance between and .
Solution:
1. Coordinates:
2. Apply the Formula:
Key Points
- Accuracy in Coordinates: Ensure coordinates are correctly placed within the formula.
- Handling Negative Values: Pay attention to negative signs to avoid calculation errors.
- Simplification: Simplify under the square root before calculating the final distance.
- Units of Measurement: Lengths are always positive and depend on the context for units.