Question

if the point A(1,2), B(0,0) and C(a,b) are collinear, then find the relation between a and b.

Answer 1

$\underline{ \underline{ \mathfrak{Answer}}} : - \\ \implies \: \boxed{b = 2a} \\ \\ \underline{ \underline{\mathfrak{Explanation}}} : - \\ \\ \underline{\underline{\mathfrak{Given}}} : -$

Points are :-

A ( 1,2) , B ( 0,0) , C ( a ,b )

let ,

$x1 = 1 \: \: ,\: y1 = 2 \\ \\ x2 = 0 \: , \: y2 = 0 \\ \\ x3 = a \: ,\: y3 = b$

According to the question-

Let given points are collinear then,

$we \: know \: that ,\\ \\ \frac{1}{2} \bigg(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) \bigg) = 0 \\ \\ replacing \: given \: values \: \\ \\ \frac{1}{2} \bigg(1(0 - b) + 0(b - 2) + a(2 - 0) \bigg) = 0 \\ \\ - b +0+ 2a = 0 \\ \\ \boxed{b = 2a} \\ \\ \red{This \: is \: the \: required \: relation \: between \: a \: and \:b}$