Coordinate geometry is thought of as one of the exciting topics of mathematics. It summarises the connection between geometry and algebra via graphs by using curves and lines. It offers geometrical techniques in algebra and allows algebra to answer geometrical equations. It is a part of geometry where the situation of the points on the plane is summarised using disconnected figures of numbers. The technique of coordinate geometry is explained together with the formulas and derivations. Coordinate geometry is summarised as the investigation of geometry with the help of a coordinate system. By using coordinate geometry, it is likely to find the distance in a:b ratio, locate the centre point of a line, evaluate the area of a triangle in the Cartesian plane, etc. Numerous terms in Cartesian geometry should be grasped properly. These terms are as follows:
a) Coordinate Geometry: It is one of the parts of geometry where the place of a point is summarised by using coordinates.
b) Coordinates are the code of ethics that helps to demonstrate the correct place of a point in the coordinate planes.
c) A coordinate plane is an analytical plane that is created by the intersection of two diagonal lines known as the x-axis and the y-axis.
d) It is used to separate any line in 2 ways in the ratio a:b.
e) This technique is to find the coordinates at which the line is separated in two equal halves.
While organising the graphs on a plane, the lists of the numbers of both direct and indirect equations are created. The straight line which is known as the Cartesian plane, is separated into four portions by two axes intersecting to each other is identified as the x-axis ( horizontal) and the y-axis( vertical). The four portions and the metamorphic value are shown as
Quadrant 1 : ( + X axis, + Y axis)Quadrant 2: ( -X axis, + Y axis)Quadrant 3: ( -X axis, -Y axis)Quadrant 4: ( + X axis, -Y axis) The point at which axes bisect each other is known as the origin. The place at any tip of a plane is shown by a set of values, and these pairs are known as the coordinates. If the coordinates are recognised, the distance between the two points and the centre point of the interims which is linked to the points may be evaluated. The gradient of the line is determined by the following formula:
Px+ Qy+ R = 0
Qy= -Px-R
or
y= -(P/Q) - (Q/R)
Connecting the above associations with y= mx+ r
The distance between the two points can be solved as follows:
Distance = Whole root {( x2-x1)^2+ (y2-y1)^2}
The distance between the two points can be solved as follows:
Distance = Whole root {( x2-x1)^2+ (y2-y1)^2}
The same aspects A & B which have coordinates ( x1,y1) and (x2, y2) independently. The coordinates of a point are shown as
M(x,y) = {(x1+x2/2), (y1+y2)/2}
The area of a triangle in coordinate geometry whose peaks are (x1,y1) , (x2,y2) and (x3,y3) is
1/2[x1(y2-y3)+ x2(y3-y1)+ x3(y1-y2)]
If the atea of a triangle whose peaks are (x1,y1), (x2,y2) and (x3,y3) is 0, then the points are symmetrical.
