Step-by-step explanation:
Co-ordinate Geometry
Coordinate Geometry is considered to be one of the most interesting concepts of mathematics. Coordinate Geometry (or the analytic geometry) describes the link between geometry and algebra through graphs involving curves and lines. It provides geometric aspects in Algebra and enables them to solve geometric problems. It is a part of geometry where the position of points on the plane is described using an ordered pair of numbers. Here, the concepts of coordinate geometry (also known as Cartesian geometry) are explained along with its formulas and their derivations.
Introduction to Coordinate Geometry
Coordinate geometry (or analytic geometry) is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc. There are certain terms in Cartesian geometry that should be properly understood. These terms include:
Coordinate Geometry Terms
Coordinate Geometry DefinitionIt is one of the branches of geometry where the position of a point is defined using coordinates.
What are the Coordinates?Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
Coordinate Plane MeaningA coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Distance FormulaIt is used to find the distance between two points situated in A(x1,y1) and B(x2,y2)
Section FormulaIt is used to divide any line into two parts, in m:n ratio
Mid-Point TheoremThis formula is used to find the coordinates at which a line is divided into two equal halves.
What is a Co-ordinate and a Co-ordinate Plane?
You must be familiar with plotting graphs on a plane, from the tables of numbers for both linear and non-linear equations. The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis (horizontal line) and the y-axis(vertical line).
The four quadrants along with their respective values are represented in the graph below-
Quadrant 1 : (+x, +y)
Quadrant 2 : (-x, +y)
Quadrant 3 : (-x, -y)
Quadrant 4 : (+x, -y)
The point at which the axes intersect is known as the origin. The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates.
