First slide

Introduction to 3-D Geometry

Question

$G (1, 1, - 2) is the centroid of the triangle ABC and D is the mid point of BC . If A = (- 1, 1, - 4) then D =$

Moderate

A

$(\frac{1}{2}, 1, \frac{- 5}{2})$
B

$(5, 1, 2)$
C

$(- 5, - 1, - 2)$
D

$(2, 1, - 1)$

Solution

Centroid G divides the median AD through A internally in the ratio 2:1
$\Rightarrow G = \frac{2 D + A}{3} \Rightarrow D = \frac{3 G - A}{2} = (2, 1, - 1)$

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