Coordinate Geometry

Board: CBSE Class: 10

Chapter Overview

Coordinate geometry uses the Cartesian coordinate system to locate points using ordered pairs (x, y). The distance between points (x1, y1) and (x2, y2) is √((x2-x1)² + (y2-y1)²). The section formula finds the coordinates of a point dividing a line segment in a given ratio. For internal division: ((mx2+nx1)/(m+n), (my2+ny1)/(m+n)). The midpoint formula is a special case of the section formula. The area of a triangle with vertices (x1, y1), (x2, y2), (x3, y3) is 1/2|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|.

Topics Covered

Cartesian System
Distance Formula
Section Formula
Midpoint Formula
Area of Triangle
Collinearity
Quadrilateral Area

Key Formulas

d = √(x2-x1)² + (y2-y1)²

P = ((mx2+nx1)/(m+n), (my2+ny1)/(m+n))

Midpoint = ((x1+x2)/2, (y1+y2)/2)

Area = 1/2|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|

Real-World Applications

Applications: GPS navigation, computer graphics, map systems, architecture, game development.

Study Tips

Tip: Memorize distance and section formulas

Tip: Practice area formula with different vertex orders

Tip: Solve NCERT exemplar problems