The document discusses Rene Descartes and the Cartesian coordinate system. It introduces Descartes as the French mathematician who first published on coordinate geometry in 1637. It then explains the Cartesian coordinate system, which uses two perpendicular axes (x-axis and y-axis) to locate points on a plane. The axes divide the plane into four quadrants, and points are specified using an ordered pair of numbers representing their distance from each axis. Examples are given of determining the coordinates of various points.

1. CO-ORDINATE
GEOMETRY
Class:IX

2. Rene
Descartes
1596-1650

3. French Mathematician
First published La Géométrie’ in 1637
Used Algebra in study of Geometry
Cartesian Co-ordinate
Represented Lines & Curves by Algebraic
Equation
Branch : Co-ordinate Geometry

4. Cartesian co-ordinate System
The position of a point
in a plane is determined
with reference to TWO
fixed mutually
perpendicular lines,
called “Co-ordinate
Axes”

5. There are 2 Axis
5
4
3
2
1
0
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1 0 1 2 3 4 5
Y
Y’
X’ X
LINE YY’ = Y LINE XX’ = X Axis
Axis

6. 0
X’
Y
Y’
X
Line XX’ = X-Axis
Line YY’ = Y-Axis
Intersection= Origin [0]

7. Quadrants
X’
X
Y
0
Y’

8. QUESTIONS
Observe the figure & write the POSITIONS of the point
E(-4,2)
M(0,3)
D(5,3)
S(4,0)
0
T(-3,-4) K(4,-4)

9. Solutions:
Points Positions
D In Ist Quadrant
M On Y-Axis
T In IIIrd Quadrant
K In IVth Quadrant
E In IInd Quadrant
S On X-Axis

10. Write Down the co-ordinate of each points E,F,G,H & T
from the figure.
Points Co-ordinates
E (1,5)
F (4,3)
G (6,-3)
T (4,-3)
H (-4,-5)
S (-5,3)
E
F
T G
H
S
0

11. Co-ordinates of Points on Axes
P
O N
Q
Points Co-ordinates
N (4,0)
M (-4,0)
O (0,0)
P (0,4)
Q (0,-4)
M
•For X-Axis (x,0)
•For Y-Axis (y,0)
•At Origin (0,0)

12. Co-ordinates of points on Axes
A
B
C D
E
O
Points Co-ordinates
A (-5,0)
B (0,4)
C (1,0)
D (4,0)
E (0,-3)
O (0,0)

13. Sign Convention
Quadrant x
Co-ordinate
y
Co-ordinate
Ist Quadrant + +
IInd Quadrant - +
IIIrd Quadrant - -
IVth Quadrant + -
+
+
-
-

14. QUESTION
On which Quadrant or on Axis do the following points
Lie?
(5,3), (-2,4), (-3,-6), (2,-5), (0,4), (-3,0)
Co-ordinates Position
(5,3) In Ist Quadrant
(-2,4) In IInd Quadrant
(-3,-6) In IIIrd Quadrant
(2,-5) In IVth Quadrant
(0,4) On Y-Axis
(-3,0) On X-Axis

15. Evaluation
Q.1) Observe the figure and write the positions of the points
P(-4,1)
Q(0,5)
S(4,0)
R(2,2)
T(-6,-3)
0
Q(5,-3)

16. Q.2) On which Quadrant or on Axis do the following
points Lie?
(1,0) (-7,3) (0,0)
(-3,4) (0,7) (-2,-6)
(1,-4) (0,-1) (3,1)
(-5,-2) (4,0) (3,-4)