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Published on March 8, 2014

Author: lajae1

Source: slideshare.net

## Description

Analytical geometry, basic concepts and calculations.

ANALYTIC GEOMETRY GRADE: 10 Lajaé Plaatjies 201248629

HISTORY Introduced in the 1630s , an important mathematical development, for it laid the foundations for modern mathematics as well as Aided the development of calculus RENE DESCARTES (1596-1650) and PIERRE DE FERMAT (1601-1665), French mathematicians, independently developed the foundations for analytical geometry

ANALYTIC GEOMETRY • A branch of mathematics which uses algebraic equations to describe the size and position of geometric figures on a coordinate system.

ANALYTIC GEOMETRY • The link between algebra and geometry was made possible by the development of a coordinate system which allowed geometric ideas, such as point and line, to be described in algebraic terms like real numbers and equations. • Also known as Cartesian geometry or coordinate geometry.

ANALYTIC GEOMETRY • The use of a coordinate system to relate geometric points to real numbers is the central idea of analytic geometry. • By defining each point with a unique set of real numbers, geometric figures such as lines, circles, and conics can be described with algebraic equations.

CARTESIAN PLANE • The Cartesian plane, the basis of analytic geometry, allows algebraic equations to be graphically represented, in a process called graphing. • It is actually the graphical representation of an algebraic equation, of any form -- graphs of polynomials, rational functions, conic sections, hyperbolas, exponential and logarithmic functions, trigonometric functions, and even vectors.

CARTESIAN PLANE • x-axis (horizontal axis) where the x values are plotted along. • y-axis (vertical axis) where the y values are plotted along. • origin, symbolized by 0, marks the value of 0 of both axes • coordinates are given in the form (x,y) and is used to represent different points on the plane.

INCLINATION OF A LINE • The smallest angle θ, greater than or equal to 0°, that the line makes with the positive direction of the xaxis (0° ≤ θ < 180°) • Inclination of a horizontal line is 0. • The tangent of the inclination m = tan θ

INCLINATION OF A LINE y y L L θ O M θ x O M x

ANGLE BETWEEN TWO LINES

ANGLE BETWEEN TWO LINES • If θ is angle, measured counter clockwise, between two lines, then • where m2 is the slope of the terminal side and m1 is the slope of the initial side

A point is an ordered pair of numbers written as (x; y). ● Distance is a measure of the length between two points. ● The formula for finding the distance between any two points is: ●

The formula for finding the mid-point between two points is:

SLOPE OF A LINE • The slope or gradient of a line describes the steepness, incline or grade. • A higher slope value indicates a steeper incline. • Slope is normally described by the ratio of the “rise” divided by the “run” between two points on a line. • The slope is denoted by

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