Published on March 8, 2014
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
MPM2D Grade 10 Math Analytic Geometry Test. Midpoint. M=((x1+x2)/(2)),((y1+y2)/(2)) Length. L=√(x2-x1)^2+(y2-y1)^2; ... CHC2D Grade 10 Academic History ...
CAMI Mathematicsathematicsathematics: Grade 10: Grade 10 ... GRADE 10_Analytical Geometry Author: teacher Created Date: 10/3/2013 1:37:09 PM
Page 113 ANALYTICAL GEOMETRY Revision of Grade 10 Analytical Geometry Let’s quickly have a look at the analytical geometry you learnt in Grade 10.
n Introduction n . Analytical geometry, also called co-ordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry ...
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Analytical geometry, also referred to as coordinate or Cartesian geometry, is the study of geometric properties and relationships between points, lines and ...
Analytical geometry is the study of geometric properties, relationships and measurement of points, lines and angles in the Cartesian plane. Geometrical ...
In analytic geometry, also known as coordinate geometry, we think about geometric objects on the coordinate plane. For example, we can see that opposite ...
CAMI Education linked to CAPS: Mathematicsathematicsathematics Grade 10 Grade 10 - 4 - that the rules also hold form,n∈Q . 22.214.171.124.3.5.7 126.96.36.199.9.2.1