(Q19) Find the value of 'b' for which the points A(1,2) , B(-1,b) and C(-3,-4) are collinear.

Solution :

Let the given points A(1, 2), B(-1, b) and C(-3, -4).

Then x1= 1,y1= 2;   x2= -1,y2= b;   x3= -3,y3= -4

We know, area of ∆ =
1
2
 |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|
area of ∆ABC =
1
2
 |1(b+)+(-1)(--)+(-3)(-b)=0| (∵ The given points are collinear)

 |b + + - +3b| = 0

 |4b + | = 0

 4b+ = 0

 ∴ b = -