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Question

Find the lengths of the medians of the triangle with vertices A(0,0,6),B(0,4,0) and (6,0,0).

Solution
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Let AD,BE and CF be the medians of the given ABC.
Since AD is the median, D is the mid-point of BC.

coordinates of point D= (0+62,4+02,0+02)=(3,2,0)

AD= (03)2+(02)2+(60)2=9+4+36=49=7

Since BE is the median, E is the mid-point of AC.

coordinates of point E= (0+62,0+02,6+02)=(3,0,3)

BE= (30)2+(04)2+(30)2=9+16+9=34

Since CF is the median, F is the mid point of AB.

coordinates of point F= (0+02,0+42,6+02)=(0,2,3)

Length of CF= (60)2+(02)2+(03)2=36+4+9=49=7

Thus the lengths of the medians of ABC are 7,34 and 7 units.

397126_418413_ans_1b3a937ea40f4763a2d3f3a99115988a.png

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