Coordinate Geometry

Coordinate Geometry Formula Sheet

Overview

Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes using their coordinates.

Key Concepts

Point

• A point is a location in a coordinate plane.
• Hindi: बिंदु (Bindu)

Coordinate Plane

• A coordinate plane is a two-dimensional plane with x and y axes.
• Hindi: संगणकीय परिक्रमा (Sangnaṇakīya Parikramā)

Distance Formula

• The distance between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)^2 + (y2 - y1)^2)
• Hindi: दूरी का सूत्र (Dūrī kā Sūtra)

Midpoint Formula

• The midpoint of a line segment joining two points (x1, y1) and (x2, y2) is given by: M = ((x1 + x2) / 2, (y1 + y2) / 2)
• Hindi: मध्यम बिंदु का सूत्र (Madhyama Bindu kā Sūtra)

Slope Formula

• The slope of a line passing through two points (x1, y1) and (x2, y2) is given by: m = (y2 - y1) / (x2 - x1)
• Hindi: ढलान का सूत्र (Dhalaṇa kā Sūtra)

Equations of Lines

Slope-Intercept Form

• The equation of a line passing through a point (x1, y1) with slope m is given by: y - y1 = m(x - x1)
• Hindi: ढलान-चुंबकीय रूप

Point-Slope Form

• The equation of a line passing through a point (x1, y1) with slope m is given by: y - y1 = m(x - x1)
• Hindi: बिंदु-ढलान रूप

General Form

• The equation of a line is given by: ax + by + c = 0
• Hindi: सामान्य रूप

Circle

Equation of a Circle

• The equation of a circle with center (h, k) and radius r is given by: (x - h)^2 + (y - k)^2 = r^2
• Hindi: वृत्त का समीकरण

Key Formulas

• Area of a triangle: A = (1/2) |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

• Hindi: त्रिभुज का क्षेत्रफल

• Area of a triangle using coordinates of vertices: A = (1/2) |(x1y2 + x2y3 + x3y1) - (x2y1 + x3y2 + x1y3)|

• Hindi: त्रिभुज के शीर्ष बिंदु का क्षेत्रफल