8
CBSE Marks
★★★★★
Difficulty
9
Topics
High
Board Weight
Topics Covered
9 key topics in this chapter
Distance Formula
Distance from Origin
Collinearity of Three Points
Section Formula (Internal Division)
Section Formula (External Division)
Mid-Point Formula
Centroid of a Triangle
Area of a Triangle
Condition: Collinear Points (Area = 0)
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Distance Formula | \(d = √[(x₂−x₁)² + (y₂−y₁)²]\) |
| Section Formula (Int) | \(P = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)]\) |
| Mid-Point | \(M = [(x₁+x₂)/2, (y₁+y₂)/2]\) |
| Area of Triangle | \(½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|\) |
| Centroid | \(G = [(x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3]\) |
Important Points to Remember
The distance from origin to point (x, y) is √(x² + y²).
Three points are collinear if and only if the area of the triangle formed is 0.
The centroid of a triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) is ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).
Section formula (external): P = [(mx₂−nx₁)/(m−n), (my₂−ny₁)/(m−n)].