For the point P(18,−17) and Q(23,−12)​, find the distance​ d(P,Q) and the coordinates of the midpoint M of the segment PQ.

Answer 1

midpoint = M(41/2,-29/2) = (20.5,-14.5)

just average the x coordinates (18/23)/2 = 20.5

and average the y coordinates (-17-12)/2 = -14.5

Put them together as the coordinates of M

distance squared = d^2 = sum of squares of the difference in the x and y coordinates

d^2 = (23-18)^2 + (-17+12)^2 = 5^2 + 5^2 = 50

d = sqr50 = 5sqr2 = about 5(1.414) = 7.07

That's the distance from P to Q

distance from P to M, or M to Q is just half that = 7.07/2 = 3.54