CO-ORDINATE GEOMETRY
Algebra and geometry are two branches of mathematics.
Solving geometrical problems with the help of algebra is
known as Coordinate Geometry or Analytical Geometry. In
other words, the branch of mathematics in which methods of
algebra are used to solve geometrical problems is known as
Coordinate Geometry or Analytical Geometry.
Cartesian Plane
Draw two lines, XOX’ and YOY’ in a plan perpendicular to each
other. The point of intersection is at point O. Using a suitable
scale, mark the points on both the lines with equal distance.
The plane so obtained is called Cartesian Plane.
x
Third Quadrant
6. Point
A point P is marked according to its distance from origin. That
means, point P(x , y ) refers to the point, which is at x distance
from y-axis and at distance y from x-axis.
So, location of a point P in Cartesian plane consists of two
parts, which are as follows: -
(ii) Ordinate
In point P(x , y ) , y is the ordinate, which is distance of point
from x-axis.
First Quadrant
0
x’
The distance of point from origin O as per x-axis is called
x coordinate.
(ii) The distance of point from origin O as per y-axis is called
y coordinate.
(i) Abscissa
In point P(x , y ) , x is the abscissa, which is the distance of
point from y-axis.
y
Second Quadrant
(i)
So, a point is located in the cartesian plane depending upon
the nature of abscissa and ordinate, i.e. whether abscissa and
ordinate are positive and negative.
y
Forth Quadrant
P(- x , y)
y’
0
x’
Here are few terms related to a point and its location in the
cartesian plane.
2. Axis
Line XOX’ is called x-axis or axis of x and line YOY’ is called yaxis or axis of y.
4. Coordinates
Any point on cartesian plane is denoted by two coordinates of
the point. That means,
x
P(- x , - y)
1. Origin
Point O is called the origin.
3. Quadrant
Four regions made by the two lines are called quadrant.
(i) YOX is first quadrant
(ii) YOX’ is second quadrant
(iii) X’OY’ is third quadrant
(iv) XOY’ is forth quadrant
P( x , y)
P( x , - y)
y’
(i)
In first quadrant, abscissa is positive and ordinate is
positive.
Point P(x , y ) will lie in first quadrant.
(ii) In second quadrant, abscissa is negative and ordinate is
positive.
Point P(− x , y ) will lie in second quadrant.
(iii) In third quadrant, abscissa is negative and ordinate is
negative.
Point P(− x , − y ) will lie in third quadrant.
(iv) In fourth quadrant, abscissa is positive and ordinate is
negative.
Point P(x , − y ) will lie in forth quadrant.
Note
1. On the origin, abscissa is 0 (Zero) and ordinate are 0
(Zero).
Point P(0, 0 ) will lie on origin.
2. If abscissa is 0 (Zero), then point will lie on y-axis.
Point P(0, y ) will lie on y-axis.
3. If ordinate is 0 (Zero), then point will lie on x-axis.
Point P(x , 0 ) will lie in first quadrant.