In the ABC A = (1, 3, -2) and G (-1, 4, 2) is the centroid of the… - Vidyadip

MCQ

In the $\Delta \text{ABC}$ A = (1, 3, -2) and G (-1, 4, 2) is the centroid of the triangle. If D is the mid point of BC then AD =

A
$\frac{\sqrt21}{2}$
✓
$\frac{3\sqrt21}{2}$
C
$\sqrt{21}$
D
$\frac{63}{2}$

✓

Answer

Correct option: B.

$\frac{3\sqrt21}{2}$

$\frac{3\sqrt21}{2}$

Solution:
First, we calculate the distance AG,
It is $(4+1+16)^{0.5}=21^{0.5}$
From the property of the centroid that it divides the line joining AD in the ratio 2 : 1.
The distance $=\text{AD}=\frac{3}{2}\text{AG}$
$\text{AD}=\frac{3}{2}{ 21}^{0.5}$

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