Page 2 - LN

Note
(i):In case of internal division,point dividing the line segement lines on it.But in external division,point
dividing the line segment does not line on it.

(ii)If a point P divides line segment AB externally in the ratio m :m
2
1

Here AP:PB=m :m
1
2

m x  m x m y  m y
Then the coordinates of point P are ( 1 2 2 1 , 1 2 2 1 )
m  m 2 m  m 2
1
1

This formula is known as section formula for external division

Mid-point formula
If P(x,y) is the mid point of the line segment AB,which divides AB in the ratio 1:1,then the coordinates of
x  x y  y
the point P(x,y) will be x= 1 2 , y = 1 2
2 2
CENTROID:-The meeting point of all medians of a triangle is known as Centroid.
CIRCUMCENTRE:-The meeting point of all perpendicular bisectors of all sides of a Triangle
is known as Circumcentre.
ORTHOCENTRE:The meeting point of all altitudes of a triangle is known as Orthocentre.
INCENTRE:The meeting point of all angle bisectors of a triangle is known as Incentre.
AP 3
Exa:1-If A and B are (1,4) and (5,2) respectively,Find the coordinates of P if 
PB 4
AP 3
Soln:  , AP:PB=3:4
PB 4

Let co-ordinates of P be (x, y),Here m1=3,m2=4,x1=1, y1=4,x2=5,y2=2
Therefore,
m x  m x m y  m y
x= 1 2 2 1 , y= 1 2 2 1
m  m 2 m  m 2
1
1

2