OA Explanation:

Don't go for Section formula (to find the coordinates of C), Mid-point formula (to find the coordinates of M and N), and then Distance Formula (to find the length of MN and BC)

All we need to do is, draw a line segment with end points A and B with C in between and closer to B

i.e. If \(BC = x\) then \(AC = 3x\)

Plot points M and N;
AM = MC = \(\frac{3x}{2}\)
CN = NB = \(\frac{x}{2}\)

Notice, MN = MC + CN = \(\frac{3x}{2} + \frac{x}{2} = 2x\)

So the required ratio = 2 : 1

Hence, option B