Question

question. Let (a, b) denote the midpoint of the line segment between P = (3, 4) and
Q = (11, 6). Find the values of a and b.

solution. (a,b) = p + 1/2(pq) =p+ 1/2(q-p)=1/2(p+q)

so I have this question that I dont really understand the solution for. I dont get how p+ 1/2(q-p) can be equal to 1/2(p+q). can anyone explain this for me?

Answer 1

PQ is the distance from P to Q. That is, it is Q-P when we use their actual coordinates.

1/2 (P+Q) is just one way of saying that the midpoint at (a,b) is just the average of the coordinates of P and Q.