Lengths of segments on number lines

Key Notes :

If the coordinate of Y is x1 and the coordinate of Z is x2 ,then the length of YZ is YZ = |x2 − x1|.

Introduction:

• Number Lines: A visual representation of numbers placed in order on a straight line.

Basic Concepts:

1. Coordinates:

• Every point on a number line has a unique coordinate.
• Positive numbers are to the right, and negative numbers are to the left of zero.

1. Length of a Segment:

• The distance between two points on a number line.
• Calculated by finding the absolute difference between the coordinates of the two points.

Calculating Lengths:

1. Formula:

• Length=∣a−b∣ where a and b are the coordinates of the endpoints.

1. Examples:

• If point A is at 3 and point B is at -2, the length of segment AB is ∣3−(−2)∣=5∣3−(−2)∣=5.

Properties:

1. Direction Matters:

• Length is always positive due to the absolute value.
• The order of the coordinates matters in the calculation.

1. Zero Length:

• If (a = b), the length is zero as the points coincide.

Applications:

1. Real-world Examples:

• Representing distances on a map.
• Measuring changes in temperature or stock prices over time.

1. Problem Solving:

• Solving problems involving distances and intervals on a number line.

Conclusion:

Understanding the lengths of segments on number lines is fundamental in mathematics. It provides a visual and quantitative way to analyze distances and relationships between points. The concept is applicable in various fields and serves as a foundation for more advanced mathematical concepts.

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