Let-A-B-and-C-be-the-midpoints-of-the-sides-BC-CA-and-AB-of-the-triangle-ABC-Prove-that-AA-1-2-AB-AC-

Question Number 16055 by Tinkutara last updated on 17/Jun/17

Let A^{'}, B^{'} and C^{'} be the midpoints of

the sides B C, C A and A B of the

triangle A B C . Prove that

\vec{{A A}^{'}} = \frac{1}{2} (\vec{A B} + \vec{A C})

Answered by mrW1 last updated on 17/Jun/17

\vec{{A A}^{'}} = \vec{AB} + \frac{1}{2} \vec{BC} \dots (i)

\vec{{A A}^{'}} = \vec{AC} + \frac{1}{2} \vec{CB} = \vec{AC} - \frac{1}{2} \vec{BC} \dots (ii)

(i) + (ii) :

2 \vec{{A A}^{'}} = \vec{AB} + \vec{AC}

\vec{{A A}^{'}} = \frac{1}{2} (\vec{AB} + \vec{AC})

Commented by Tinkutara last updated on 17/Jun/17

Thanks Sir!