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analytical  Coordinate that divide the line segment internally or externally
Coordinate that divide the line segment internally or externally
Ratio is used to find the coordinates of a point P which divides the segment joining the points A and B internally or externally in the ratio m : n.
Formulae: 
Coordinate that divide the segment externally, 
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Example:
Find the coordinate of the line joining the point (3,4) and (5,6), that divide the linesegment iexternally in the ratio of 3:4.
m=3,n=4,x1=3,y1=4 and x2=5, y2=6
(3*5 4 * 3)/(34),(3*6 4 *4)/(34)
(15 12)/(1),(18 16)/(1)
(3,2

Coordinate that divide the segment internally, 
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Example:
Find the coordinate of the line joining the point (3,4) and (5,6), that divide the line segment internally in the ratio of 3:4.
m=3,n=4,x1=3,y1=4 and x2=5, y2=6
(3*5 +4 * 3)/(3+4),(3 *6 +4 *4)/(3+4)
(15 +12)/(7),(18 +16)/(7)
(27/7,34/7
(3.9,4.9)

