Question

If the points(0,0),(1,2) and (a,b) are collinear, then find the relation between a and b ?

Answer 1

I have solved it by using the property that collinear points have same slope
As they line on the same line

Answer 2

Answer:  The answer is b = 2a.

Step-by-step explanation: Given that the points (0, 0), (1, 2) and (a, b) are collinear.

We are to find the relation between 'a' and 'b'.

We know that if three points are collinear, then the area of the triangle formed by them is equal to 0 units.

Also, if A(p,q), B(r,s) and C(t, h) aree any three collinear points, then we must have

$p(s-h)+r(h-q)+t(q-s)=0.$

Therefore, for the given three points (0, 0), (1, 2) and (a, b) to be collinear, we must have

$0(2-b)+1(b-0)+a(0-2)=0\\\\\Rightarrow 0+b-2a=0\\\\\Rightarrow b-2a=0\\\\\Rightarrow b=2a.$

Thus, the required relation is b = 2a.