Question

In the $\Delta$ 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. $\frac{\sqrt{21}}{2}$
• B. $\frac{3\sqrt{21}}{2}$
• C. $\sqrt{21}$
• D. $\frac{63}{2}$

Answer 1

The correct option is B $\frac{3\sqrt{21}}{2}$

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$AD=\frac{3}{2}$AG
Hence,$AD=\frac{3}{2}{21}^{0.5}$