Q29 of 45 Page 1

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is

Intercept form of plane is



Now distance of plane (1) from (0,0,0) is-





squaring both sides-



Now for the locus of the centroid we must have


x = (a/3), y = (b/3) & z = (c/3)


⇒ a = 3x, b = 3y & c = 3z


∴ equation (2) becomes






Hence Proved.


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