Question

If the points $A(1,2),O(0,0)$ and $C(a,b)$ are collinear, then

• A. $a=b$
• B. $a=2b$
• C. $2a=b$
• D. $a=-b$

Answer 1

The correct option is C $2a=b$

Let the given points $A(x_1,y_1)=(1,2),O(x_2,y_2)=(0,0)\&C(x_3,y_3)=(a,b)$ are collinear.

Then $ar\Delta AOC$ should be zero.

Now, $ar\Delta AOC=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

$ar\Delta AOC=\frac{1}{2}[1(0-b)+0(b-y_1)+a(2-0)]=\frac{1}{2}(-b+2a)$

Therefore,

$\frac{1}{2}(-b+2a)=0$

$\Rightarrow 2a=b$

Ans- Option C