Free Study Material For RRB Examination
Subject : Mathematics (Coordinate of Geometry)
Coordinate Geometry is also called Analytical Geometry.
It is that branch of geometry in which we use two numbers called coordinates to
indicate the position of a point in a plane.
Cartesian Coordinate System
The horizontal line x´ is called the x-axis and the vertical
line y´ oy is called the y-axis and together they are called the coordinate
axes. The point of intersection of these two axes is called the origin. Let P be
any point in a plane. From P draw perpendiculars to the coordinate axes meeting
the x-axis in M and y-axis in N. Here, OM(x) is the x-coordinate or absicssa of
a point P. Similarly, ON(y) is the y-coordinate or ordinate of point P.
This position of the point P in the plane with respect to the
coordinate axes is represented by the ordered pair (x, y) and this system is
called the cartesian coordinate system.
The coordinates of the origin O are (0, 0). Also, x´ox and y´oy divide the plane
into four regions called quadrants.
1. xoy is quadrant I. Here, x-coordinate is positive and
y-coordinate is positive. (+,+)
2. x´oy is quadrant II. Here, x-coordinate is negative and y-coordinate is
positive. (–, +)
3. x´o is quadrant III. Here, x-coordinate is negative and y-coordinate is
negative. (–, –)
4. xoy´ is quadrant IV. Here, x-coordinate is positive and y-coordinate is
negative. (+, –)
(1,5) lies in first quadrant
(–2,3) lies in second quadrant
(–2, –4) lies in third quadrant
(4,–2) lies in fourth quadrant
The coordinate of origin is (0, 0).
The ordinate of every point on x-axis is 0.
The ordinate of every point on y-axis is 0.
Distance between Two Points : Let P(xl,yl) and Q (x2,y2)
be any two points on the plane, then the distance between P and Q is represented
as PQ is given by