|
Unlimited Tutoring & Homework Help
|
|
Introduction
Rene' Descartes' (1596-1665), a French philosopher and mathematician, introduced a method by which the position of a point can be corresponded with an ordered pair of real numbers. These pair of real numbers are called the Coordinates. This method is the new idea of combining two branches of mathematics, Algebra and Geometry. The combination of these two branches of mathematics was called Algebraic Geometry, Coordinate Geometry or Analytical Geometry.
Coordinates
The coordinates of a point are quantities, which determine the position of the point. If for instance, a point P lies somewhere on a straight line XX', then its position may be defined by a single number.
Rectangular Coordinate System
The position of a point in a plane is determined by two coordinates.
Quadrants
The four quadrants formed by the ordinate axes.
Distance Formula
The length of the line segment AB, which joins A (x1, y1) and B (x2, y2).
Section Formula
To find the co-ordinates of a point C (x, y) which divides the line segment joining the two points A (x1,y1) and B (x2,y2) in the ratio m:n ( internally and externally).
Area of the Triangle
If the coordinates of the vertices of the DABC are A(x1,y1), B(x2,y2) and C(x3,y3).
Locus and its Equations
When a point moves so as to always satisfy a given condition, or conditions, the path it traces out is called its locus under these conditions.
Slope
The slope of a line is defined as the tangent of the angle made by the line with the x-axis in the positive direction (anti-clockwise).
Parallel and PerpendicularLinesn
Two lines are perpendicular if the product of their slopes is -1 or slope of one line is the negative reciprocal of the other.
Summary
In coordinate geometry, the tools of algebra are used in studying geometry by establishing 1-1 correspondence between the points in a plane and the ordered pairs of real numbers.
