Chapter 7 — Coordinate Geometry

NCERT Class 10 Maths Chapter 7 covers Coordinate Geometry, teaching students how to find the distance between two points using the Distance Formula and how to find the coordinates of a point dividing a line segment in a given ratio using the Section Formula.

Chapter 7 of NCERT Class 10 Mathematics introduces Coordinate Geometry as an algebraic tool for studying geometry. Students learn the Distance Formula — PQ = √[(x₂–x₁)² + (y₂–y₁)²] — derived using the Pythagoras theorem, which finds the distance between any two points on a plane. The chapter then covers the Section Formula, which gives the coordinates of a point dividing a line segment joining A(x₁,y₁) and B(x₂,y₂) internally in the ratio m₁:m₂. A special case of the Section Formula yields the midpoint formula: ((x₁+x₂)/2, (y₁+y₂)/2). Applications include identifying collinear points, classifying triangles and quadrilaterals, and locating equidistant points.

1. 01Distance Formula: the distance between P(x₁,y₁) and Q(x₂,y₂) is √[(x₂–x₁)²+(y₂–y₁)²], derived from the Pythagoras theorem.
2. 02Distance of a point P(x,y) from the origin O(0,0) is √(x²+y²).
3. 03Section Formula: the point dividing segment AB — where A is (x₁,y₁) and B is (x₂,y₂) — internally in ratio m₁:m₂ has coordinates ((m₁x₂+m₂x₁)/(m₁+m₂), (m₁y₂+m₂y₁)/(m₁+m₂)).
4. 04Midpoint Formula (special case of Section Formula with ratio 1:1): midpoint of AB is ((x₁+x₂)/2, (y₁+y₂)/2).
5. 05Three points are collinear if the sum of the distances between the two pairs of adjacent points equals the distance between the outermost pair.
6. 06Coordinate geometry links algebra and geometry, with applications in physics, engineering, navigation, seismology, and art.