The Cartesian Plane

The Cartesian Plane is a two-dimensional coordinate system defined by a horizontal x-axis and a vertical y-axis, facilitating the representation and analysis of geometric figures.

Coordinate System

The section introduces the Cartesian coordinate system, which serves as the foundation for analyzing geometric figures using algebra.

Distance Between Two Points

This section introduces the distance formula used to calculate the distance between two points in a Cartesian coordinate plane.

Formula

Midpoint Of A Line Segment

This section covers the concept of calculating the midpoint of a line segment joining two points in a Cartesian coordinate system.

Formula

Gradient (Slope) Of A Line

The gradient (slope) of a line quantifies its steepness and direction, determined by the vertical and horizontal change between two points.

Formula

This section introduces crucial formulas in coordinate geometry, covering distance, midpoint, gradient, and the equations of lines.

Equation Of A Line

This section covers the equation of a line, including its general form and how to derive it using two points.

General Form

This section introduces the fundamental concepts of Coordinate Geometry, including understanding the Cartesian plane, calculating distances, determining midpoints, gradients, and line equations.

Equation Using Two Points

This section explains how to derive the equation of a straight line from two points using slope and point form.

Parallel And Perpendicular Lines

This section explores the concepts of parallel and perpendicular lines, detailing their characteristics in relation to gradients.

Parallel Lines

This section covers the properties of parallel lines in coordinate geometry, focusing on their equal gradients.

Perpendicular Lines

This section covers the definition and properties of perpendicular lines in the context of Coordinate Geometry.

Application In Geometry

This section discusses the application of coordinate geometry in determining collinearity and calculating the area of triangles.

Collinearity

Collinearity refers to the condition where three or more points lie on a single straight line.

Area Of A Triangle (Coordinate Geometry)

This section introduces the formula for calculating the area of a triangle using the coordinates of its vertices in the Cartesian plane.

Summary

Coordinate Geometry combines algebra and geometry using the Cartesian plane, enabling us to solve practical geometric problems.

Exercises

This section provides a series of exercises designed to reinforce key concepts in Coordinate Geometry, including distance, midpoint calculations, equations of lines, and properties of collinear points.