Question

# If the points A(1,2), B(0,0) and C(a,b) are collinear, then which of the following is correct   a = b a = 2b 2a = b 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(y2−y3)+x2(y3−y1)+x3(y1−y2)]∴Δ=12[1(0−b)+0(b−2)+a(2−0)]=12(−b+0+2a)=12(2a−b) 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(2a−b)=0⇒2a−b=0⇒2a=b Hence, the required relation is 2a = b.

Suggest corrections