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

If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle

1.	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» 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. \(\sqrt{(5-2)^2+(4-5)^2+(6-5)^2} = \sqrt{(3)^2+(-1)^2+(1)^2} = \sqrt{11}\).

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