Question

If the centroid of triangle whose vertices are $(a,1,3),(-2,b,-5)$ and $(4,7,c)$ be the origin, the value of $c-a-b$ is___

Answer 1

Coordinates of centroid of a triangle is

Coordinates of the centroid $G\equiv (\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})$

$O=\frac{a-2+4}{3}$

$\Rightarrow a=-2$

$O=\frac{1+b+7}{3}$

$\Rightarrow b=-8$

And $O=\frac{3-5+c}{3}$

$\Rightarrow c=2$

$c-a-b=2-(-2)-(-8)$

$=2+2+8=12$

$c-a-b=12$