Question

How do you find the point on the line y = x so that the distance from that point to the point (18, 0) is a minimum?

Answer 1

Call P the point (18, 0) and Q the point (x, y) where the perpendicular from P meets the line y = x.

The triangle OPQ is a right isosceles triangle with 2 angles of 45 deg.

Then x = y = 18/2 = 9#

The point Q (9, 9) is the answer.