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Question

If the points A(1,2), B(0,0) and C(a,b) are collinear, then which of the following is correct
 


  1. a = b

  2. a = 2b

  3. 2a = b

  4. a = –b


Solution

The correct option is C

2a = b


Let the given points are A = (x1,y1)=(1,2)
B=(x2,y2)=(0,0) and C=(x3,y3)=(a,b).
Area of Δ ABC
=Δ=12[x1(y2y3)+x2(y3y1)+x3(y1y2)]Δ=12[1(0b)+0(b2)+a(20)]=12(b+0+2a)=12(2ab)
Since, the points A(1,2), B(0,0) and C(a,b) are collinear, then area of the triangle ABC should be equal to zero.
i.e, area of Δ ABC = 0
12(2ab)=02ab=02a=b
Hence, the required relation is 2a = b.

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