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Question

# If the point (a,âˆ’1),(2,1) and (4,5) are collinear. Then, the value of a is

A
1
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B
2
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C
3
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D
4
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Solution

## The correct option is B 1If three or more points lie on the same straight line then the points are collinearSince, points lie on the same straight line, the area covered by them is zero.Three points make a triangle. Therefore, the area of the triangle is zeroWe know that area of the triangle is 12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))Given collinear points are (a,−1),(2,1),(4,5)⟹12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))=0⟹a(1−5)+2(5−(−1))+4(−1−1)=0⟹−4a+12−8=0⟹4a=4⟹a=1

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