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If the points (a ,\ 0),\ (0,\ b)a n d\ (...

If the points `(a ,\ 0),\ (0,\ b)a n d\ (1,\ 1)` are collinear, prove that `a+b=a bdot`

Text Solution

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Given: `(a ,\ 0),\ (0,\ b)a n d\ (1,\ 1)`
Then we have to show that `a+b=a b`
Then the condition of collinearity is given as:
`x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0`
As we given that points are collinear then
`a(b-1)+0(1-0)+1(0-b)=0`
`ab-a-b=0`
`a+b=ab`
...
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Knowledge Check

  • If the points (a, 0), (0, b) and (1, 1) are collinear, then

    A
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  • If the points (a , 0) (0 , b) and (1 , 1) are collinear , then (1)/(a) + (1)/(b) is :

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