Question

In a parallelogram ABCD, the diagonals AC and BD intersect at point M. If P is the mid-point of side AD, then PM is equal to ______.

Options

• AB

• `1/2 AB`

• `1/3 AB`

• `1/4 AB`

Answer 1

In a parallelogram ABCD, the diagonals AC and BD intersect at point M. If P is the mid-point of side AD, then PM is equal to `underlinebb(1/2 AB)`.

Explanation:

In a parallelogram, the diagonals bisect each other.

So, M is the midpoint of AC.

Let AB = vector b and AD = vector d.

Then `M = (b + d)/2` while P (midpoint of AD) = `d/2`. 

So, PM = M – P

= `(b + d)/2 - d/2`

= `b/2`

= `1/2 AB`