Question

A plane meets the coordinate axes in A, B, C such that the centroid of the triangle ABC is the point (a, a, a).
Then the equation of the plane is x + y + z = p, where p is

• A. $a$
• B. $\frac{3}{a}$
• C. $\frac{a}{3}$
• D. $3a$

Answer 1

The correct option is D $3a$

$\because$ Equation of plane x + y + z = p
$\therefore \frac{x}{p}+\frac{y}{p}+\frac{z}{p}=1$
$\therefore$ Coordinates of A, B, C are
(p, 0, 0), (0, p, 0) and (0, 0, p) respectively.
$\because$ Centroid of $\Delta$ ABC is (a, a, a)
$\therefore$ $a=\frac{p}{3}$
$\Rightarrow p=3a$