Question

A plane meets the coordinate axes at points A, B and C, such that the centroid of a triangle ABC is \((2,-\frac{2}{3},\frac{1}{2})\). The perpendicular distance from the origin to this plane is...

• A. \(\frac{6}{\sqrt{26}}\)
• B. \(\frac{5}{\sqrt{26}}\)
• C. \(\frac{4}{\sqrt{26}}\)
• D. \(\frac{3}{\sqrt{26}}\)

Hint:

Centroid coordinates are one third of the intercepts.

Answer 1

The Correct Option is A

Step 1: Use the intercept formula
Distance from origin $=\frac{1}{\sqrt{\frac1{a^2}+\frac1{b^2}+\frac1{c^2}}}=\frac{1}{\sqrt{\frac1{36}+\frac14+\frac49}}$.
The sum is $\frac{1+9+16}{36}=\frac{26}{36}$, so $d=\frac{6}{\sqrt{26}}$.

Final Answer:
Option (A). \[ \boxed{\text{(A)}} \]