reading this quesn mite make u feel this is a 9th class quesn(it atleast made me feel so:P) but still cudnt do it:P
now i realise why my maths is weak........kaash 9th mein dhang se padh leta:P
In a triangle OAB , E is the mid-pt. of OB and D is a pt. on AB uch that AD:DB = 2:1 . If OD and AE intersect at P , determine the ratio OP:PD.
1when u go to XII you'll learn a very easy method for this in vectors, OP:PD is equal to 3:2
6lol
:D
i am a dropper..........
and i know how to do it in vectors
but i want to know how it can be solved in coordinate...
11simply consider the base am along the x axis with the coordinate a at the origin .
Now assume coordinates as given below
A(0,0)
B(α,0)
O(β,ξ)
now coordinate E is(α+β/2),
D(2α/3,0)
Equation AE=y=ξ/α+βx
OD:-y=ξ/3β-2α/3(x-2α/3)
Solving the two equations THE Y coordinate of the point is 2ξ/5
NOW if the ratio is k:1
THEn
ξ/k+1=2ξ/5
1/k+1=2/5
solving k=3/2
Thus ratio is 3:2
THIS CAN BE SOLVED BY GEOMETRY ALSO.