Using vector operations, Prove the line segment joining the midpoints of two sides of a triangle

Question

Show, using vector operations, that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and has half its length.

Answer 1

Say vertices are A,B,C. Midpoint of AB is given by $(A+B)/2$. Midpoint of BC is given by $(B+C)/2$. So the vector joining these midpoints is $(A+B)/2-(B+C)/2=(A-C)/2$, i.e. is parallel to the vector $A-C$ and has half its length.