Question

If the plane $7x+11y+13z=3003$ meets the axes in $A,B,C$, then the centroid of $\Delta ABC$ is

• A. $(143,91,77)$
• B. $(143,77,91)$
• C. $(91,143,77)$
• D. ($143,66,91)$

Answer 1

Answer: (A)

$(143,91,77)$

intercept form $\frac{7x}{3003}+\frac{11y}{3003}+\frac{13z}{3003}=1$

$\therefore A[429,0,0],B[0,273,0],C[0,0,231]$ are the vertices of triangle ABC.

then centroid is $(\frac{429+0+0}{3}+\frac{273}{3}+\frac{237}{3})$

$⟹(143,91,77)$