The slide show helps me to introduce Coordinate Geometry in Secondary School level.

1. How much is the distance between
flower and the butterfly ?

3. x- axis
-5
-4
-3
-2
-1
0
1
2
3
4
5
6

4. 2
3
Y- axis
1
0
-1
-1
-2
-2
-3
-3
Origin
0
1
(0,0)
-4
x- axis
-5
-4
2
3
4
5
6

5. 3
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
1st quadrant
1
2
3
4
5
6

6. 3
1st quadrant
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
2nd quadrant
1
2
3
4
5
6

7. 3
1st quadrant
-3
-2
-1
0
1
2
3
4
5
6
-3
3rd quadrant
-2
-1
-4
-4
-5
0
1
2
2nd quadrant
4th quadrant

8. 3
1
2
To mark a point on a plane (3, 0)
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
(3, 0)
1
2
3
4
5
6

9. 3
2
1
To mark a point on a plane (-5, 0)
0
0
-1
-1
-2
-2
-3
-3
-4
(-5, 0)
-5
-4
1
2
3
4
5
6

10. 3
-4
-3
-2
-1
0
1
-1
-5
0
1
2
( 0,3)
-4
-3
-2
To mark a point on a plane ( 0,3)
2
3
4
5
6

11. 3
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
To mark a point on a plane ( 0,-1)
1
( 0,-1)
2
3
4
5
6

12. 3
2
1
A
What are the co-ordinates of A ?
0
0
-1
-1
-2
-2
-3
-3
-4
-4
-5
1
2
3
4
5
6

13. 3
To mark a point on a plane (4, 2 )
-4
-3
-2
-1
0
-1
-5
0
1
2
(4, 2)
1
2
3
-4
-3
-2
4 is x coordinate or abscissa
2 is y coordinate or ordinate.
4
5
6

14. 2
3
(3,3)
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
To mark a point on a plane (3,3 )
1
2
3
4
5
6

15. 3
(3,3)
1
2
1st quadrant
0
0
-1
-1
-2
-2
-3
-3
-4
-4
-5
1
2
3
4
5
6

16. 3
1
2
(-3,3)
0
To mark a point on a plane (-3,3 )
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
1
2
3
4
5
6

17. 3
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
2nd quadrant (-3,3)
1
2
3
4
5
6

18. -2
-1
0
-1
-3
-2
(-4,-2)
-3
-4
-4
-5
0
1
2
3
To mark a point on a plane (-4,-2)
1
2
3
4
5
6

19. 3
2
1
-2
-1
0
-3
0
-1
-4
-3
-2
(-4,-2)
3rd quadrant
-4
-5
1
2
3
4
5
6

20. -1
0
1
2
3
4
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
3
To mark a point on a plane (3,-2)
(3,-2)
5
6

21. 3
2
1
0
-1
0
1
2
3
4
5
6
-1
-2
-2
-3
-3
-4
-4
-5
4th quadrant
(3,-2)

22. 3
(-3,-1)
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
What is the coordinates of shown point?
1
2
3
4
5
6

23. 3
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
What is the coordinates of shown point?
1
2
3
4
5
6

24. 3
-1
0
-1
-2
-2
-3
-3
-4
-4
-5
0
1
2
What is the coordinates of shown point?
1
2
3
4
5
6

25. 2
3
A
1
-3
-2
-1
0
-4
0
1
2
3
4
5
6
-3
-2
-1
What are the coordinates of vertices of the tria
-4
-5
C
B

26. 3
2
1
-2
-1
0
-3
0
1
2
3
4
5
6
-1
-4
-3
-2
What are the coordinates of vertices of the star
-4
-5

27. 3
(3,3)
2
To mark a point on a plane (3,3 )
-1
0 (0,0)1
-1
-2
-2
-3
-3
-4
-4
-5
0
1
Let there is a flower at this point.
2
3
4
5
6

28. (3,3)
Let there is a butterfly at (1,1)
(1,1)
(0,0)

29. How much is the distance between
flower and the butterfly ?
(1,1)
(3,3)

30. B
(3,3)
A (1,1)
O
Let A is the position of the Butterfly.A has co-ordinates (1,1).
B is the position of the flower.B has the coordinate ( 3, 3).

31. B
(3,3)
C
A (1,1)
O
P
Q
Let us draw the perpendiculars AP on X axis ,BQ on Y axis.
AC on BQ to complete a right triangle ABC.

32. In Triangle ABC ,
the length of AC = PQ
PQ = OQ – OP =3 – 1 =2
the length of BC =BQ - CQ
=3 – 1 =2
(1,1)
A
In Right Triangle ABC ,
O
P
2
2
2
AC = AB + BC
AC = AB 2 + BC 2
AC = 2 + 2 = 4 + 4 = 8 = 2 2
2
2
B
(3,3)
C
Q

33. B (x , y )
2
2
A
( x1 , y1 )
O
How much is the distance between
the points A and B ?

34. B
( x2 , y 2 )
( x1 , y1 )
A
O
P
C
Q
Perpendiculars AP and BQ on X axis are drawn..
AC on BQ are drawn to complete a right triangle ABC.

35. B
( x2 , y 2 )
OP = x1
OQ = x2
y2 − y1
PQ = x2 - x1
AC = x2 - x1
BQ = y2
OQ = y1
BC = y2 - y1
y2
A
(x , y )
1
O
1
x1 P
x2 − x1
x2
x2 − x1
C
y1
Q

36. B
( x2 , y 2 )
.
AC = x2 − x1
BC= y2 − y1
y2 − y1
A
( x1 , y1 )
O
x1 P
x2 − x1
x2
x2 − x1
C
Q

37. B
( x2 , y 2 )
AC = x2 − x1
BC= y2 − y1
AC = AB + BC
2
2
2
AC = AB2 + BC 2
AC = (x 2 − x1 ) 2 + (y 2 − y1 ) 2
d = (x 2 − x1 ) 2 + (y 2 − y1 ) 2
y2 − y1
( x1 , y1 )
A
O
P
x1
x2 − x1
C
x2 − x1
Q
x2

38. B (x , y )
2
2
It is called distance formula.
A
( x1 , y1 )
O
The distance between the points A ( x1 , y1 )
and B ( x2 , y2 )
d = ( x2 − x1 ) + ( y2 − y1 )
2
2

39. B (x , y )
2
2
C is a point on the line joining
A and B in ratio
m:n
A
( x1 , y1 )
O

40. m:n
C ( x, y )
m
A and B in ratio
n
C is a point on the line joining
B (x , y )
2
2
A
( x1 , y1 )
What will be co-ordinates of C?

41. n
( x2 , y2 )B
y2 − y
x2 − x
S
m
( x, y ) C
( x1 , y1 ) A
O
x1
x − x1
Q
R
N
M
x
y − y1
P
x2
Perpendiculars AM,CN , BP AR CS Are drawn.
y2 − y1

42. n
( x2 , y2 )B
m
Triangle ACQ and
BCS are similar.
( x1 , y1 ) A
AC AQ
=
BC CS
O
x1
y2 − y
x2 − x
S
( x, y ) C
x − x1
x2
Q
y2 − y1
R
N
M
x
y − y1
P
m x − x1
⇒ =
⇒ mx2 − mx = nx − nx1
n x2 − x
⇒ mx + nx = nx1 + mx2 ⇒ x(m + n) = nx1 + mx2
nx1 + mx2
⇒x=
( m + n)

43. n
( x2 , y2 )B
m
Triangle ACQ and
BCS are similar.
( x1 , y1 ) A
AC AQ
=
BC CS
O
x1
y2 − y
x2 − x
S
( x, y ) C
x − x1
Q
y2 − y1
R
N
M
x
y − y1
P
x2
m y − y1
⇒ =
⇒ my2 − my = ny − ny1
n y2 − y
⇒ my + ny = ny1 + my2 ⇒ y (m + n) = ny1 + my2
ny1 + my2
⇒y=
( m + n)

44. This is called section formula B
C ( x, y )
m:n
A
m
A and B in ratio
n
C is a point on the line joining
( x2 , y 2 )
( x1 , y1 )
The co-ordinates of C are :
nx1 + mx2
x=
( m + n)
ny1 + my2
y=
( m + n)

45. in ratio
n
C is an exterior point point on
the line joining A and B
B (x , y )
2
2
m:n
A
C ( x, y )
m
( x1 , y1 )
The co-ordinates of C are :
nx1 − mx2
x=
( m − n)
ny1 − my2
y=
( m − n)

46. Co-ordinates of circumcentre OF A TRIANGLE
WHEN VERTICES ARE GIVEN
B( x2 , y2 )
0
A
( x1 , y1 )
C
x1 + x2 + x3
x=
3
( x2 , y 2 )
y1 + y2 + y3
y=
3

47. Co-ordinates of in -centre OF A
TRIANGLE WHEN VERTICES ARE GIVEN
B( x2 , y2 )
c
a
0
A
( x1 , y1 )
b
C
( x2 , y 2 )
ax1 + bx2 + cx3 ay1 + by2 + cy3
x=
y=
3
3

48. ASSIGNMENT
Q1.Which point on x axis is equidistant from
(5,9) and (-4,6)?
Q2. Which point on y axis is
equidistant from (2,3) and (-4,1)?

49. ASSIGNMENT
Q3.Prove that (2a,4a),(2a,6a)and (2a+√3a) are vertices of an
equilateral triangle.
Q4.In what ratio the x-axis divide the line segment joining
the points (2,-3) and (5,6)?

50. ASSIGNMENT
Q5. For what value of x will the points (x,1),(2,1) and (4,5)
lie on a line?
Q6. Determine the ratio in which the line 3x+y-9=0 divides
the segment joining the points (1,3) and (2,7)?

51. ASSIGNMENT
Q7If the points (-2,-1), (1,0),(x,3) and ( 1,y) form a
parallelogram, find the value of x and y.
Q8.Find the coordinates of (i) centroid ii)incentre
(iii)circumcentre of of the triangle whose
vertices are (0,6),(8,12) and ( 8,0)

52. Thank You
Developed by Pratima Nayak,
Kendriya Vidyalaya,Fort Willia,Kolkata