For locating the position of a point on a plane, we require a pair of coordinate axes.
X and Y Axes
The left-right (horizontal) direction is commonly called X or The distance of a point from the y-axis is called its x-coordinate, or abscissa.
The up-down (vertical) direction is commonly called Y or The distance of a point from the x-axis is called its y-coordinate, or ordinate.
The coordinates of a point on the x-axis are of the form (x, 0), and of a point on the y-axis are of the form (0, y).
The point where x-axis and y-axis intersect is called the origin. Its coordinates are (0,0).
The ordinates of all points on a horizontal line which is parallel to x-axis are equal i.e. y = constant = 2.
The abscissa of all points on a vertical line which is a line parallel to y-axis are equal i.e. x = constant = 4.
Four Quadrants of Coordinate Plane
The rectangular axes X’OX and Y’OY divide the plane into four quadrants as below :
The coordinates of the points in the four quadrants will have sign according to the below table:
The distance between two points (x1, y1) and (x2, y2) in a rectangular coordinate system is equal to
The distance of a point (x, y) from origin is
A point P(x,y) which divide the line segment AB in the ratio m1 and m1 is given by
The mid point P is given by
Remark : To remember the section formula, the diagram given below is helpful:
Area of Triangle ABC
Area of triangle ABC of coordinates A(x1,y1) , B(x2,y2) and C(x3,y3) is given by
For point A,B and C to be collinear, The value of A should be zero, i.e. A=0.
How to solve general Problems of Area in Coordinate Geometry
|Area of Triangle||Three vertices will be given, you can calculate the area directly using formula|
|Area of Square||Two vertices will be given, we can calculate either side or diagonal depending on vertices given and apply the square area formula|
|Area Of rhombus||Given: all the vertices coordinates
1) Divide the rhombus into two triangle. Calculate the area of both the triangle and sum it
2) Calculate the diagonal and apply the Area formula
|Area of parallelogram||Three vertices are sufficient to find the area of parallelogram
Calculate the area of the triangle formed by the three vertices and double it to calculate the area of parallelogram
|Area of quadrilateral||Given: all the vertices coordinates
Divide into two triangle. Calculate the area separately and sum it