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 Q.

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

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

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

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

This question was posed to me by my college director while I was bunking the class.

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

Answer 1

Correct choice is (c) \(\sqrt{11}\)

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 PR is (5, 4, 6).

Length of median through Q is distance between midpoint of PR and Q i.e. \(\sqrt{(5-2)^2+(4-5)^2+(6-5)^2} = \sqrt{(3)^2+(-1)^2+(1)^2} = \sqrt{11}\).