Question

If two vertices of a triangle $ABC$ are $A(-1,2,4)$and $B(2,-3,0)$,and the centroid is $(2,0,2)$ then the vertex $C$ has the coordinates

• A. $(5,1,2)$
• B. $(1,-\frac{1}{3},\frac{7}{3})$
• C. $(3,-\frac{2}{3},\frac{5}{3})$
• D. none of these

Answer 1

The correct option is A $(5,1,2)$

Let $C$ be $(a,b,c)$
By using the formula of centroid of triangle, we get
$G(2,0,2)=(\frac{-1+2+a}{3},\frac{2-3+b}{3},\frac{4+0+c}{3})$

$⟹(2,0,2)=(\frac{1+a}{3},\frac{b-1}{3},\frac{4+c}{3})$

Comparing the coordinates we get

$\frac{a+1}{3}=2,\frac{b-1}{3}=0,\frac{4+c}{3}=2$

$⟹a=5,b=1,c=2$
Hence, $C=(5,1,2)$