# Misc 2 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 2 Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0). Let Δ ABC where AD, BE, CF are medians Since median bisects the opposite side D is Midpoint of BC E is Midpoint of AC F Midpoint of AB Calculating AD A (0, 0, 6) D (3, – 2, 0) AD = x2−x12+y2−y12+z2 −z12 Hence x1 = 0, y1 = 0, z1 = 6 x2 = 3, y2 = – 2, z2 = 0 AD = 3−0)2+(2−02+0−62 = 3)2+(22+−62 = 9+4+36 = 49 = 7 Lenth of median AD = 7 Calculating BE B (0, 4, 0) E (3, 0, 3) BE = x2−x12+y2−y12+z2 −z12 Hence x1 = 0, y1 = 4, z1 = 0 x2 = 3, y2 = 0, z2 = 3 BE = 3−0)2+(0−42+3−02 = 3)2+(−42+32 = 9+16+9 = 34 Length of median BE = 34 Calculate CF C (6, 0, 0) F (0, 2, 3) CF = x2−x12+y2−y12+z2 −z12 Hence x1 = 6, y1 = 0, z1 = 0 x2 = 0, y2 = 2, z2 = 3 CF = 0−6)2+(2−02+3−02 = −6)2+(22+32 = 36+4+9 = 49 = 7 The Length of median CF = 7

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