If the points A(1, 2), O(0, 0), and C(a, b) are collinear, then which of the following relations is true?

Since the points $(1, 2)$, $(0, 0)$, and $(a, b)$ are collinear, the area of the triangle formed by them must be zero. Alternatively, the slope of the line passing through $(1, 2)$ and $(0, 0)$ must equal the slope of the line passing through $(0, 0)$ and $(a, b)$. Slope $\frac{2-0}{1-0} = \frac{b-0}{a-0} \implies 2 = \frac{b}{a} \implies b = 2a$.