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 = 0

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Solution

Given points are (1,2), (0,0) and (a,b).

These points are collinear if their slopes are equal.

Now, slope of AB $= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{0 - 2}{0 - 1} = 2$

and slope of BC= $\frac{b - 0}{a - 0} = \frac{b}{a}$

So, $\frac{b}{a} = 2$

$\Rightarrow b = 2 a$

So, the correct choice is (c).

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