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Question

The points (a,0),(0,b) and (1,1) are collinear. Then the value of 1a+1b is

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Solution

Let A=(a,0),B=(0,b) and C=(1,1) and B divides the line segment AC in the ratio of k:1.
Then, by section formula,
(k+ak+1,kk+1)=(0,b)k=a

Now, kk+1=b
a1a=ba1a=1b1a+1b=1

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