Question:
Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).
Answer:
Given points A (0,0,6) B(0,4,0) and C(6,0,0)
Let D is the mid point of BC
E is the mid point of AB
and F is the mid point of AC
Now D = {(0+6)/2 , (4+0)/2 , (0+0)/2 } = (3,2,0)
E = {(0+0)/2 , (4+0)/2 , (0+6)/2 } = (0,2,3)
F = {(0+6)/2 , (0+0)/2 , (0+6)/2 } = (3,2,3)
Now
AD = √{(3-0)2 + (2-0)2 + (0-6)2 } = √{9 + 4 + 36 } = √49 = 7
BE = √{(0-0)2 + (2-4)2 + (3-0)2 } = √{0 + 4 + 9 } = √13
CF = √{(3-6)2 + (0-0)2 + (3-0)2 } = √{9 + 0 + 9 } = √18 = 3√2
So AD = 7
BE = √13
CF = 3√2
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