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प्रश्न
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
विकल्प
- \[\frac{1}{3}\]
- \[- \frac{1}{3}\]
- \[\frac{2}{3}\]
- \[- \frac{2}{3}\]
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उत्तर
We have three collinear points A(k, 2k) : B(3k, 3k) : C (3, 1) .
In general if `A(x_1 , y_1) ; B (x_2 ,y_2) ; C(x_3 ,y_3) `are collinear then, area of the triangle is 0.
`x_1 (y_2 - y_3 ) + x_2 (y_3 - y_1) + x_3 (y_1- y_2 ) = 0`
So,
`k (3k - 1 ) + 3k(1 - 2k) + 3 (2k - 3k) = 0`
So,
-3k2 - k = 0
Take out the common terms,
-k (3k + 1) = 0
Therefore,
`k = -1/3`
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