Post on 08-Jul-2015
description
CO-ORDINATE
GEOMETRY
Class:IX
Rene
Descartes1596-1650
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
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”
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 XX’ = X AxisLINE YY’ = Y
Axis
0X’
Y
Y’
X
Line XX’ = X-Axis
Line YY’ = Y-Axis
Intersection= Origin [0]
Quadrants
X’X
Y
Y’
0
QUESTIONS
Observe the figure & write the POSITIONS of the point
E(-4,2)
M(0,3)
D(5,3)
S(4,0)
T(-3,-4) K(4,-4)
0
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
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
O N
P
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)
Co-ordinates of Points on Axes
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)
Sign Convention
Quadrant x
Co-ordinate
y
Co-ordinate
Ist Quadrant + +
IInd Quadrant - +
IIIrd Quadrant - -
IVth Quadrant + -
+
+
-
-
On which Quadrant or on Axis do the following points
Lie?
(5,3), (-2,4), (-3,-6), (2,-5), (0,4), (-3,0)
QUESTION
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
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)
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)