Q94 / 160 · AP EAMCET 2004 · Mathematics

If the plane $3 x-2 y-z-18=0$ meets the coordinate axes in $A, B, C$ then the centroid of $\triangle A B C$ is

  • A
    $(2,3,-6)$
  • B
    $(2,-3,6)$
  • C
    $(-2,-3,6)$
  • Correct answer
    D
    $(2,-3,-6)$

Solution

Given equation $3 x-2 y-z=18$ can be rewritten as $$ \begin{aligned} \frac{x}{18 / 3}-\frac{y}{18 / 2}-\frac{z}{18} & =1 \\ \frac{x}{6}-\frac{y}{9}-\frac{z}{18} & =1 \end{aligned} $$ $\therefore$ Points of a coordinates axes are $A(6,0,0), B(0,-9,0)$ and $C(0,0,-18)$. $\therefore$ Centroid of a triangle $$ \begin{aligned} & =\left(\frac{6+0+0}{3}, \frac{0-9+0}{3}, \frac{0+0-18}{3}\right) \\ & =(2,-3,-6) \end{aligned} $$

Hence, the correct answer is option: 'D'.

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