Q1
The distance formula is derived from the:
APythagoras theorem
Bmid-point theorem
Csection formula
Dquadratic formula
CBSEClass 10 (CBSE)MathematicsCh 7 · Topic 1
The Distance Formula
Learning to calculate the distance between two points on a coordinate plane.
Core concept
For example, the distance between points (2,3) and (5,7) is calculated as √[(5-2)² + (7-3)²] = √[9+16] = √25 = 5 units. This formula has wide applications, from calculating the length of a line segment in geometry problems to determining the actual distance between two locations on a map when their coordinates are known, and even in more advanced fields like computer graphics and physics for calculating distances between points or objects.
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• Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²].
• This formula is derived from the Pythagoras theorem applied to coordinate differences.
• Example: distance between (2,3) and (5,7) is √[9+16]=√25=5 units.
• Applications include geometry problems, mapping, and computer graphics.