Coordinate Geometry – Class 10 Maths Chapter 7: Distance & Section Formula
Class 10 Coordinate Geometry notes: distance formula, section formula, midpoint, area of triangle, collinearity for CBSE & ICSE boards.
Chapter 7: Coordinate Geometry
7.1 Distance Formula
The distance between two points P(x₁, y₁) and Q(x₂, y₂) is:
Example: Distance between A(3, 4) and B(7, 1):
AB = √[(7−3)² + (1−4)²] = √[16 + 9] = √25 = 5 units
Distance from origin: For point P(x, y): OP = √(x² + y²)
7.2 Section Formula
If a point P(x, y) divides the line segment joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m : n, then:
y = (my₂ + ny₁) / (m + n)
7.3 Midpoint Formula
The midpoint of the line segment joining A(x₁, y₁) and B(x₂, y₂) is a special case of the section formula with m:n = 1:1:
7.4 Area of a Triangle
The area of a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃) is:
If the area = 0, then the three points are collinear (lie on the same straight line).
Example: Find the area of triangle with vertices (1, 2), (4, 6), (7, 2).
Area = ½ |1(6−2) + 4(2−2) + 7(2−6)| = ½ |4 + 0 − 28| = ½ × 24 = 12 sq. units
Indexed Topics & Examination Keywords
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