Class 10 · Coordinate Geometry
Distance Formula
Complete Suite
Four interactive modules to master the distance formula — from derivation to advanced problem solving.
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Module 1
Derivation of
Distance Formula
Step-by-step visual derivation using Pythagoras theorem on a coordinate plane.
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Module 2
Find the
Value of x
Practice finding hypotenuse, perpendicular and base of right triangles using Pythagoras.
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Module 3
Find the
Distance
Calculate distances between coordinate pairs using the distance formula step by step.
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Module 4
Long
Questions
Advanced multi-part problems: triangles, circles, rhombuses, rectangles and more.
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Derivation of Distance Formula
Derivation of Distance Formula
Step-by-Step Derivation
Step 1 Plot the Points
Mark the two points on the coordinate plane:
Step 2 Draw Perpendiculars
- From point A, draw a perpendicular to the x-axis — meets at point P.
- From point B, draw a perpendicular to the x-axis — meets at point Q.
- From A, draw a horizontal line to meet the vertical from B at point C.
Triangle ABC is a right-angled triangle (right angle at C).
Step 3 Identify Lengths
From the diagram:
- OP = x₁, AP = y₁
- OQ = x₂, BQ = y₂
Therefore:
AC = x₂ − x₁ (horizontal distance)
BC = y₂ − y₁ (vertical distance)
Step 4 Apply Pythagoras Theorem
In right triangle ABC:
AB² = AC² + BC²
Substituting values:
AB² = (x₂ − x₁)² + (y₂ − y₁)²
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