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)