Mathematics – Analytic Geometry
All geometry problems are solved graphically. Using algebra and geometry together, the same problems can be solved with calculations using variables. Vectors are mathematical objects with length and direction.
They can be represented by arrows placed on a coordinate system and denoted by letters set in boldface or with tiny arrows on top. They are used to describe physical quantities.
Mathematics – Coordinate geometry
In coordinate geometry every point is allotted a fixed place in the coordinate system around a selected set of axes. A set of points can be represented by equations or using graphs.
If you are in a new city you can orient yourself using a fixed reference point and find out the direction and distance between this place and your next destination. In a coordinate system points are specified using a pair of numbers that describe the distance and direction from your fixed reference point, or origin.
The origin is where two selected perpendicular axes intersect (0, 0). The coordinates (3. 4) would therefore refer to a point three units to the right of and four units above the origin.
A point set
A straight line is an infinite number of points. The equation y = 2x + 3 describes a straight line and can be used to define the set of points in the line. By substituting a value for x, the value of y can be found, defining the coordinates of a point.
Any coordinates of a point (x. y) on a straight line will satisfy the equation.
Geometry and algebra
Geometry and algebra work well together. Algebra can describe and solve a geometric problem; geometry can be used to find the solution to an algebraic equation. In cases where an exact solution is impossible or too difficult to obtain, graphs are frequently used.
Both geometry and algebra answer the question of how many points are common to two sets of points. Coordinate geometry is very important in mathematics and is a vital tool for physics; for instance it is possible to graphically depict movement of an object by choosing time as the independent variable.
CARTESIAN COORDINATE SYSTEMS
A Cartesian or rectangular coordinate system includes two perpendicular axes that form a plane, as well as coordinate lines that are at equal distances from each other. A value along the horizontal axis is called an x-coordinate or abscissa, while a value on the vertical axis is called a y-coordinate or ordinate.
The point at which the axes cross, with the coordinates (0,0), is called the origin. This system was named after its inventor, the French philosopher Rene Descartes, who also investigated the fields of algebra and Euclidean geometry.
The idea was also developed at the same time by Pierre de Fermat, although Fermat did not publish his finding. Today, the Cartesian system is the most widely used coordinate system, since it offers the most effective way to represent geometric concepts such as scalar products
BASICS
A FUNCTION gives exactly one y-value In the output set for each x-value In the Input set.
A LINEAR FUNCTION will produce a straight line If all the pairs (x, y) are plot ted on a graph.