Consider points P = (0, a), Q = (c, b) in the plane, with a, b, c all positive.

Question

Consider points P = (0, a), Q = (c, b) in the plane, with a, b, c all positive. Find a point R = (x, 0) so that the distance P R+QR is minimal. Justify that your answer is indeed a minimum.

Answer 1

PR + QR is minimal when PR = QR, i.e. R is the midpoint of PQ.

Can you determine the mid point?