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Question
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
Options
−3
7
2
-2
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Solution
We have three collinear points A(1,2) ;B(-5,6) ;C(a, - 2).
In general if `A(x_1 ,y_1) ;B(x_2 , y_2) ;C(x_3 ,y_3)` are collinear then,
`x_1(y_2 - y_3 ) + x_2 (y_3 - y_1) + x_3(y_1-y_2) = 0`
So,
1(6 + 2) - 5(- 2-2)+ a (2 -6 ) = 0
So,
-4a + 8 + 20 = 0
Therefore,
a = 7
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