Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry, is a branch of mathematics that uses algebraic equations to describe geometric figures on a coordinate plane.

Basic Concepts

1. Coordinate Plane: The coordinate plane, also known as the Cartesian plane, is a two-dimensional plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis).

2. Coordinates: Every point in the coordinate plane can be identified by a pair of numbers (x, y), where x represents the horizontal distance from the origin and y represents the vertical distance from the origin. This pair of numbers is known as the coordinates of the point.

3. Distance Formula: The distance between two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula: √[(x₂ - x₁)² + (y₂ - y₁)²]

4. Midpoint Formula: The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by: [(x₁ + x₂)/2 , (y₁ + y₂)/2]

Applications

Coordinate geometry allows us to translate geometric shapes into algebraic expressions and equations, making it easier to solve complex geometric problems. It is used extensively in various fields of mathematics, physics, computer graphics, and engineering. It also forms the basis for calculus and other advanced mathematical studies.