Question

A plane meets the coordinate axes at A, B, C such that the centroid of $\Delta$ABC is (a, b, c). Show that the equation is $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3$.

Answer 1

Let $(h,0,0),(0,k,0),(0,0,l)$ be points $A,B,C$ on $x,y,z$ axis,line meets at $A,B,C$ on $x,y,$ and $z$ axis.

$\therefore$ Equation of plane in intercept form,

$\frac{x}{h}+\frac{y}{k}+\frac{z}{l}=1$

Centroid $\left(G\right)=(\frac{h}{3},\frac{k}{3},\frac{l}{3})=(a,b,c)$

$\therefore h=3a,k=3b,l=3c.\therefore \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3$