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would any1 mind giving me the proof of the section formula????????

Hi!
Here is the proof of the section formula.
 
Consider any two points A (x1, y1) and B (x2, y2) and assume that P (x, y) divides AB internally in the ratio m: n i.e. PA: PB = m: n
Draw AR, PS and BT perpendicular to the x-axis. Draw AQ and PC perpendiculars to PS and BT respectively.
 
 
In ∆PAQ and ∆BPC
∠PAQ = ∠BPC    (pair of corresponding angles)
∠PQA = ∠BCP    (90°)
Hence, ∆PAQ ∼ ∆BPC  (AA similarity criterion)
 
Hope! You got the concept.
 
Cheers!
 

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Definition : If P be any point on the line AB between A and B then we say that P divides segment AB AB internally in the ratio AP: PB Also, if P be any point on the line AB but not between A and B (P may be to the right or the left of the points A, B ) then P divides AB externally in the ratio AP: PB

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absolutely correct but writing such long proofs is really a piece of hardwork. i have also posted various long answers in this site and so i know how difficult it is to write for so long and we also have to think over it. but i think the experts are at advantage as they have even symbols for sq roots and can show division easily.

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