Question

If a plane meets the coordinate axes at \( A, B, C \) such that the centroid of the triangle is \( (1, 2, 4) \), then the equation of the plane is?

• A. \( x + 2y + 4z = 12 \)
• B. \( x + 2y + 4z = 3 \)
• C. \( x + 2y + 4z = 10 \)
• D. \( x + 2y + 4z = 4 \)

Hint:

To find the equation of a plane given the centroid, use the relationship between the centroid and the coordinates of the plane's intersection with the axes.

Answer 1

The Correct Option is A

Using the centroid condition and the coordinates of the centroid \( (1, 2, 4) \), we can derive the equation of the plane by substituting the values into the general equation of a plane.