Answer to Question #158329 in Geometry for Ama Sarkodie-Addo

Question

ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x

and AC = 2y, express the vectors (i) BC, (ii) PQ, (iii) PC, (iv) BQ in terms of x

and y. What can you deduce about the directed line-segments BC and PQ?

Answer 1

(Everything below is vectors)

So, as 2x + BC = 2y, we get BC = 2y - 2x

As x + PQ = y, we get PQ = y - x

As x + PC = 2y, we get PC = 2y - x

As 2x + BQ = y, we get BQ = y - 2x

Something we can deduce about the directed line-segments BC and PQ is that

BC = 2PQ, so they are parallel.