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the point (a+1,1) , (2a+1,3) and (2a+2,2a) are collinear, if: (A)a= -1,2 (B)a= ½,2 (C)a= 2,1 (D)a= -½,2

the point (a+1,1)  , (2a+1,3) and (2a+2,2a) are collinear, if:
(A)a= -1,2
(B)a= ½,2
(C)a= 2,1
(D)a= -½,2

Grade:12

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
Hello student,
The points (a+1,1) , (2a+1,3) and (2a+2, 2a) are collinear if
\begin{vmatrix} a+1 & 1&1 \\ 2a+1& 3& 1\\ 2a+2&2a &1 \end{vmatrix} = 0
By solving this we get,
(a + 1)(3 - 2a) – 1(2a + 1 – 2a – 2) + (4a2 + 2a – 6a – 6) = 0
2a2 - 3a – 2 = 0
This gives 2a (a – 2) + 1(a - 2) = 0
a = -1/2, 2.

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