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# Question 3 Prove that the points (a,0), (b,0) and (1,1) are collinear if 1/a+1/b=1.

Asked by 28th February 2013, 10:32 AM
Sometimes there can be printing mistakes in the book of sample papers also. If you will try to solve it using the section method and try to find the ratio, you will find that the ratio would come out to be 0 if you consider the points that you provided, which is not possible for collinear points. So, yeah, there can be mistakes everywhere. Sometimes NCERT books (even Board exam papers) also have mistakes, so, its alright.

If the question as I said would have been "Prove that the points (a,0), (0,b) and (1,1) are collinear if 1/a+1/b=1.", then you can solve it as

Let A(a,0), B(0,b) and C(1,1) be the 3 collinear points
Let B divide the line segment joining AC in the ratio of k:1
Then, by section formula, the coordinates of B would be given by (k+a/k+1 , k/k+1)
However, we already know that the coordinates of B is (0,b)

So, equating, 0 = k+a/k+1 i.e. k = -a
Also, b = k/k+1
Substituting k = -a, we get
b = -a/-a+1
i.e. 1/b = a-1/a
i.e. 1/b = 1-1/a
i.e. 1/a+1/b = 1
Hence, proved
Answered by Expert 28th February 2013, 6:35 PM
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