Question

If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle then find the length of median through P.

(a) \(\sqrt{24}\)

(b) \(\sqrt{38}\)

(c) \(\sqrt{11}\)

(d) \(\sqrt{53}\)

This question was addressed to me during an interview.

Origin of the question is Three Dimensional Geometry in section Three Dimensional Geometry of Mathematics – Class 11

Answer 1

Right answer is (b) \(\sqrt{38}\)

To explain I would say: We know, midpoint of (x1, y1, z1) and (x2, y2, z2) is ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2).

Midpoint of line QR is (5, 5, 4).

Length of median through P is distance between midpoint of QR and P i.e. \(\sqrt{(5-2)^2+(5-3)^2+(4-9)^2} = \sqrt{(3)^2+(2)^2+(-5)^2} = \sqrt{38}\)