FIND THE DISTANCE OF THE CENTROID OF TRI (ABC) WHOSE VERTICES ARE A(a,0,0),B(0,b,0) C(0,0,c) FROM THE ORIGIN - Maths - Introduction to Three Dimensional Geometry

Question

FIND THE DISTANCE OF THE CENTROID OF TRI (ABC) WHOSE VERTICES
ARE A(a,0,0),B(0,b,0) C(0,0,c) FROM THE ORIGIN?

Tushar Kohli · Accepted Answer

Co-ordinates of the centroid of the triangle is given by:

$(\frac{a + 0 + 0}{3}, \frac{0 + b + 0}{3}, \frac{0 + 0 + c}{3}) = (\frac{a}{3}, \frac{b}{3}, \frac{c}{3})$

Distance of the centroid from the origin is given by:

$\sqrt{(\frac{a}{3} - 0)^{2} + (\frac{b}{3} - 0)^{2} + (\frac{c}{3} - 0)^{2}} = \frac{1}{3} \sqrt{a^{2} + b^{2} + c^{2}}$

FIND THE DISTANCE OF THE CENTROID OF TRI (ABC) WHOSE VERTICES ARE A(a,0,0),B(0,b,0) C(0,0,c) FROM THE ORIGIN?