Question

1. x-axis divides the line segment joining points (6, 4) and (1, −3) in the ratio 1 : 1.
2. If the points A (6, 1), В (8, 2), С (9, 4), and D (p, 3), taken in order, are the vertices of a parallelogram, then p = 7.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

⇒ For (i) the x‑axis meets the segment (6, 4) (1, −3) at parameter `4/7`, giving ratio 4 : 3, not 1 : 1.

⇒ For (ii), AB = (2, 1) and DC = (9 − p, 1);

Equating gives 2 = 9 − p,

So p = 7,

Hence, only the (ii) statement is valid from both statements.