Tuesday, 12 November 2013

formulas used in coordinate geometry

Distance between two points
Let P (x1, y1) and Q (x2, y2) be the two points. We have to find PQ.

OM = x1, PM = y1 = RN
ON = x2, QN = y2
PR = MN = ON – OM
= x2 – x1
QR = QN – RN = y2 – y1
By Pythagoras theorem
PQ2 = PR2 + QR2
= (x2 - x1)2 + (y2 – y1)2
If x1 = 0, y1 = 0, x2 = x and y2 = y
Then 
Section Formula
Let P (x, y) divided a line AB such that AP : PB = m1 : m2.
Let coordinates of A are (x1, y1) and B are (x2, y2).



It is obvious that

Taking, 


Similarity 
Note
(i) if P is mid point of AB, then AP : PB = 1 : 1
(ii) If m1 : m2 = k, then coordinates of P are