COORDINATE GEOMETRY CLASS 9TH

1. COORDINATE
GEOMETRY

2. Coordinate Geometry is a branch of Mathematics which deals
with the position of an object lying in a plane, described with
the help of two mutually perpendicular lines.
INTRODUCTION
The method of describing the locations
of points in a plane in this way was
described by the French Mathematician
Rene Descartes (1596 – 1650).
In honor of his work, the coordinates of a
point are often referred as Cartesian
coordinates and the coordinate plane as
Cartesian Coordinate Plane

3. The system used to describe the position of a point in a plane, is
called Cartesian System.
CARTESIAN SYSTEM
In Cartesian system, there are two mutually
perpendicular straight lines XXʹ and YYʹ
which intersect each other at point.
The point of intersection of these two lines
is called Origin and is denoted by O.
The horizontal line XOXʹ is called X – axis.
The vertical line YOYʹ is called Y – Axis.
Directions OX and OY are called Positive
directions of X and Y – axes, respectively.
Similarly, Directions OXʹ and OYʹ are called Negative
directions of X and Y – axes, respectively.

4. Note:
CARTESIAN SYSTEM
2. Any Line perpendicular to the x – axis is
parallel to y – axis.
3. Any line perpendicular to the y – axis is
parallel to the x- axis.
1. The angle between the horizontal axis
and the vertical axis is 90𝑜

5. The intersection of X and Y – axes divides the plane into four parts.
QUADRANTS
(i) XOY is called the I quadrant.
Thus, the plane which consists of two axes
and four quadrants is known as XY – Plane or
Cartesian Plane or Coordinate plane and the
axes are known as Coordinate Axes.
Each part is called Quadrant and these quadrants are numbered I, II, III
and IVth in anti-clockwise direction starting from OX.
(ii) XʹOY is called the II quadrant.
(iii) XʹOYʹ is called the III quadrant.
(iv) XOYʹ is called the IV quadrant.

6. To locate a point in a cartesian plane, its perpendicular distances from X and Y –axes are required.
COORDINATES OF A POINT IN CARTESIAN PLANE
Each point has two coordinates:
These are called coordinates of a point.
x-coordinate And y - coordinate
X
Y
X ʹ
Y ʹ
P
O
N
M
x-coordinate
Or Abscissa
y-coordinate
or
Ordinate
Perpendicular distance
from x – axis.
Perpendicular distance
from y – axis.
( x, y)
The x – coordinate of a point is its
perpendicular distance from the Y-axis
measured along x-axis. It is also known as
Abscissa.
The y – coordinate of a point is its
perpendicular distance from the X-axis
measured along y-axis. It is also known as
Ordinate.

7. 1. Every point on the x – axis has no perpendicular distance from the x – axis,
So its ordinate is 0.
Thus, the coordinates of every point on the x – axis are of the form (x, 0)
2. Every point on the y – axis has no perpendicular distance from the y – axis,
So its Abscissa is 0.
Thus, the coordinates of every point on the y – axis are of the form (0, y)
Some Important Points
3. The coordinates of a point at origin has no perpendicular distance from both
the axes. So, its abscissa and ordinate are both 0 and 0.
Thus, the coordinates of origin are (0, 0)

8. Some useful rules to determine the signs of coordinates of a point in a quadrant are
given below:
Sign Conventions of Coordinates in Different Quadrants
1. As the first quadrant is enclosed by positive x-axis and
positive y – axis, so the sign of the coordinates in the first
Quadrant are of the form (+, +)
2. As the second quadrant is enclosed by negative x-axis
and positive y – axis, so the sign of the coordinates in the
second Quadrant are of the form (-, +)
3. As the third quadrant is enclosed by negative x-axis
and negative y – axis, so the sign of the coordinates in
the third Quadrant are of the form (-, -)
4. As the fourth quadrant is enclosed by positive x-axis
and negative y – axis, so the sign of the coordinates in
the fourth Quadrant are of the form (+, -)

9. Tabular Form of Sign Convention of Coordinates in Different Quadrants
REGION QUADRANT NATURE OF
X AND Y
AXIS
SIGN OF
X -
COORDINATE
SIGN OF
Y-
COORDINATE
COORDINATES
OF A POINT
XOY I X > 0
Y>0 + + (+, +)
XʹOY II X < 0
Y > 0 - + (- , +)
XʹOYʹ III X < 0
Y < 0 - - ( - , -)
XOYʹ IV X > 0
Y < 0 + - (+, -)