Question

A triangular plane $ABC$ with centroid $(1,2,3)$ cuts the coordinates axes at $A,B,C$ respectively.

What are the intercepts made by the plane $ABC$ on the axes?

• A. $3,6,9$
• B. $1,2,3$
• C. $1,4,9$
• D. $2,4,6$

Answer 1

The correct option is A $3,6,9$

$A=(x,0,0),B=(0,y,0),C=(0,0,z)$

Centroid of the triangle ABC = $(\frac{x+0+0}{3},\frac{0+y+0}{3},\frac{0+0+z}{3})$

Hence $(\frac{x}{3},\frac{y}{3},\frac{z}{3})=(1,2,3)$

$\therefore$ The intercepts made by the plane $ABC$ on the axes are $(x,y,z)=(3,6,9)$