Coordinate Geometry class 9th powerpoint presentation by akshat upadhyay

it is a pdf of class 9th ch 3 coordinate geometry

1. Developed by Pardeep Rani
PGT Maths – JNV Chandigarh

2. CHAPTER - 3
COORDINATE GEOMETRY

3. CONTENT :

•Why Coordinate Geometry ?
•Activities from Routine Life
•History of Coordinate Geometry
•Cartesian System , Axes and Quadrants
•Plotting of a Point in the Plane if its
coordinates are given

4. Why Coordinate Geometry ?
•Locate points on paper
•Maps are based on
coordinate geometry
•Construction field
•Plot graphs in finance
•Various subjects
(Astrophysics , Chemistry
Molecules )
•Airplane Navigation
0
2
4
6
Series 1
Series 2
Series 3

5. Why Coordinate Geometry ?
•Create animations & video
games
•MRI , Citi Scan , Xray in
medical
•In other words , we can
say that Coordinate
Geometry is useful in
various fields of our
routine life .

6. Situations from our Routine Life :
•1. In the adjoining
figure , there is a main
road running in the
East-West direction and
streets with
numbering from West
to East . Each street
have house numbers
marked on it .

7. Situations from our Routine Life :
•To look for a friend’s
house here , situated in the
2
nd
street and has the
number 5 on it , first we
will have to identify the 2
nd

street and then the house
numbered 5 on it. Here , H
shows the location of the
house .
•Similarly , P shows the
location of the house
corresponding to Street
number 7 and House
number 4.

8. LOCATION OF A POINT
•Suppose you put a dot
on a sheet of paper. If
you have to tell its
location , may be you
reply : ‘the dot is in the
upper/ lower half of the
paper’ , or ‘ the dot is
near the left / right edge
of the paper’. But it will
not fix the position of
the dot precisely.

9. LOCATION OF A POINT
•Whereas to fix the
position of the dot you
need two independent
transformations e.g. the
dot is nearly 5 cm away
from the left edge of
the paper and at a
distance of 9 cm from
the bottom line of the
paper.

10. ACTIVITY FROM ROUTINE LIFE
•To make it more interesting , we
may perform the following
classroom activity known as
‘Seating Plan’ :
•Draw a plan of seating in your
classroom , putting all the desks
together , representing each
desk by a square . Write the
name of the student occupying
the desk in each square. Sonia
(S) is occupying the position
(4,1). Filled(blue) block
represents the position (5,3).

11. ACTIVITY FROM ROUTINE LIFE
Thus , Position of each student in the classroom is
described precisely by two independent
informations :
(i) the column in which she or he sits ,
(ii) the row in which she or he sits .
From the above situations and activities , we can
conclude that the position of any object lying in a
plane can be presented with the help of two
perpendicular lines. This idea gave rise to a very
important branch of Mathematics known as
Coordinate Geometry.

12. History of Coordinate Geometry
Rene Descartes , the great
French mathematician of the
seventeenth century , solved
the problem of describing the
position of a point in a plane .
His method was a development
of the older idea of latitude and
longitude . In honor of
Descartes, the system used for
describing the position of a
point in a plane, is also known
as the Cartesian System.

13. Cartesian System
•As you have already studied in the chapter Number
System , On the number line ,equal distances from
fixed point (origin-0) are marked positively in one
direction and negatively in the other. The point in
the positive direction at a distance of r units from
the origin represents the number r and the point in
the negative direction at a distance of r units from
the origin represents the number –r as shown in the
figure :

14. AXES IN THE CARTESIAN PLANE
•Descarte invented the
idea of placing two such
lines perpendicular to
each other on a plane
such that one of them is
horizontal and the
other vertical, named
as X’X (x-axis)and YY’ (y-
axis) respectively as
described in the figure :

15. AXES AND QUADRANTS OF A PLANE
•Observe that the axes
(plural of axis) divide the
plane into four parts
named as quadrants
numbered as I , II , III and
IV anticlockwise from OX.
So plane consisting of the
axes and the quadrants is
called Cartesian or the
Coordinate Plane or the
xy-plane. The axes are
called coordinate axis.

16. SIGNS OF x and y in QUADRANTS
•Quadrant I is represented
by XOY , here x and y both
are positive .
•Quadrant II is represented
by X’OY , here x is negative
and y is positive.
•Quadrant III is represented
by X’OY’ , here x and y both
are negative.
•Quadrant IV is represented
by XOY’ , here x is positive
and y is negative.

17. Abscissa & Ordinate
•In the adjoining graph , you
find that :
•(i) The perpendicular
distance of P from y-axis
measured along the positive
direction of the x-axis is PN
= OM = 4 units
•(ii) The perpendicular
distance of P from x-axis
measured along the positive
direction of the y-axis is PM
= ON = 3 units

18. Abscissa & Ordinate
•(iii)The perpendicular distance
of Q from y-axis measured
along the negative direction of
the x-axis is OR = SQ = 6 units
•The perpendicular distance of
Q from x-axis measured along
the negative direction of the y-
axis is OS = RQ = 2 units
•Here , the x – coordinate of a
point is its perpendicular
distance from the y-axis
measured along the x-axis. For
the point P , it is 4 and for Q it
is -6. the x – coordinate is
called the Abscissa .

19. Abscissa & Ordinate
•The Y – coordinate of a point is
its perpendicular distance from
the x-axis measured along the
y-axis. For the point P , it is 3
and for Q it is -2. the y –
coordinate is called the
Ordinate .
•In stating the coordinates of a
point in the coordinate plane,
the x- coordinate comes first ,
and then the y-coordinate .
Coordinates are placed in open
( round) brackets .
•Hence , the coordinates of P
are (4,3) and Q are (-6,-2).

20. •Every point on the x- axis
has zero distance from x –
axis , so the y-coordinate of
every point lying on x-axis
is always zero i.e.
coordinate of every point
on x-axis are of the form
(x,0). Similarly ,coordinates
of every point on y-axis are
of the form (0,y).
•Coordinates of Origin
Origin has zero distance
from both the axes so that
its abscissa and ordinate are
both zero. Therefore , the
coordinates of origin are
(0,0).


(0,0)

21. •EXAMPLE : In the adjoining figure,
•(i) The coordinates of B are (-5,2).
•(ii) The coordinates of C are (5,-5).
•(iii) The point identified by the
coordinates (-3,-5) is E .
•(iv) The point identified by the
coordinates (2,-4) is G.
•(v) The abscissa of the point D is 6.
•(vi) The ordinate of the point H is -3
.
•(vii) The coordinates of the point L
are (0,5).
•(viii) The coordinates of the point
M are (-3,0).

22. Plotting of a Point in the Plane
•Let the coordinates of the given
point be (3,5).
•We know that x-coordinate i.e.
abscissa represents distance of
point from y- axis , so first we
will move 3 units from origin
towards positive direction of x -
axis and then y-coordinate i.e.
ordinate being distance of point
from x – axis , we will move 5
units from that position
towards positive direction of y –
axis. This location will represent
the point (3,5).
•Similarly , we can plot point (5,-
4) and as many points as we
want .

23. •Example : Plot the points
(5,0), (0,5), (2,5),(5,2) ,(-3,-5)
, (-3,5) , (5,-3) and (6,1) in
the Cartesian plane.
•From the above example and
many more like this , we can
conclude that the position of
(x,y) is different from the
position of (y,x) for x ≠ y .
i.e.
• (x,y) ≠ (y,x) for x ≠ y and
(x,y) = (y,x) for x = y

24. Independent Practice for the students :
•In which quadrant or on which axis do each of
the points (-2,4) , (3,-1) , (-1,0) , (1,2) , (-3,-5)
and (4,0) lie ? Verify your answer by locating
them on the Cartesian plane.