Question

A plane meets the coordinate axes at A, B, C so that the centroid of the triangle ABC is (1, 2, 4). Then the
equation of the plane is​

Answer 1

Answer:

First of all we need to know what is the meaning of centrod.

The centroid is the intersection of the three medians. The three medians also divide the triangle into six triangles, each of which have the same area. The centroid divides each median into two parts, which are always in the ratio 2:1. A B 2 + B C 2 + C A 2 = 3 ( G A 2 + G B 2 + G C 2 )

If A plane meets the coordinate axes at A, B, C so that the centroid of the triangle ABC is (1, 2, 4).

Then the  equation of the plane is​ :

4x + 2y + z + 12