In triangle OPQ, O is the origin, $\overrightarrow{OP}$ = **p** and $\overrightarrow{OQ}$ = **q**. M is the midpoint of PQ. What is the position vector of M?

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Question

In triangle OPQ, O is the origin, $\overrightarrow{OP}$ = **p** and $\overrightarrow{OQ}$ = **q**. M is the midpoint of PQ. What is the position vector of M?

Accepted Answer

$\frac{1}{2}$(**p** + **q**) — Award 1 mark for correct application of midpoint formula. The position vector of the midpoint is the average of the position vectors of the endpoints. A is incorrect — this gives half the vector from Q to P. C is incorrect — this does not represent the midpoint. D is incorrect — this is not the correct midpoint formula.

Answer

**p** + $\frac{1}{2}$**q**

Answer

$\frac{1}{2}$(**p** − **q**)

Answer

**q** − $\frac{1}{2}$**p**

Answer

$\frac{1}{2}$(**p** + **q**)

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