Coordinate Geometry
Distance formula, section formula, and area of triangle in coordinate plane.
Chapter Overview
Class 10 Coordinate Geometry applies algebra to the plane. You use the distance formula, section formula (internal and external division), and area of a triangle given vertices — essential for board exams.
Distance and Section
Distance
d = √[(x₂−x₁)² + (y₂−y₁)²]
Section (internal)
P divides AB in ratio m:n → ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
Mid-point
((x₁+x₂)/2, (y₁+y₂)/2) when m:n = 1:1
Area of Triangle
Area
Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
- Collinear points give area zero
- Take absolute value for positive area
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Distance
Find distance between A(1, 2) and B(4, 6).
- 1d = √[(4−1)² + (6−2)²]
- 2= √[9 + 16] = √25
Answer
5 units
Example 2: Mid-point
Find mid-point of segment joining (−2, 3) and (4, −1).
- 1Mid-point = ((−2+4)/2, (3+(−1))/2)
- 2= (1, 1)
Answer
(1, 1)
Key Points to Remember
- ✓ Distance is always non-negative
- ✓ Section formula works for internal division (m, n > 0)
- ✓ Area formula uses determinant method
Exam Tips
- • Draw points on rough graph for orientation
- • Simplify radicals in distance answers
- • Verify collinearity using area = 0
Practice MCQs — Coordinate Geometry
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Distance of (0,0) from (3,4) is: