Discussion Forum

if a plane meets the coordinate axes at A, B and C  such that the centroid of the triangles is (1,2,4) , then the equation of te plane is 

Answer:

Explanation:

Let the equation of the plane is 

$\frac{x}{\alpha}+\frac{y}{\beta}+\frac{z}{\gamma}=1$

Then, A($\alpha$,0,0) , B(0,$\beta$, 0),and C(0,0,$\gamma$) are the points on the coordinates axes, The centroid of the triangle is (1,2,4)

$\therefore$     $\frac{\alpha}{3}=1 \Rightarrow \alpha=3$

$\frac{\beta}{3}=2 \Rightarrow  \beta=6$

and $\frac{\gamma}{3}=2 \Rightarrow  \gamma=12$

$\therefore$  The equation of the plane is 

  $\frac{x}{3}+\frac{y}{6}+\frac{z}{12}=1$

$\Rightarrow$   $4x+2y+z=12$