ABC is a Delta such A,B,C are at a distance 5 units from the origin. If `((1)/(3)-(1)/(3))` is the centroid of `DeltaABC` then the orthocentre is

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A,B anc C, then the locus of the centroid of Delta ABC is :

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

A plane a constant distance p from the origin meets the coordinate axes in A, B, C. Locus of the centroid of the triangle ABC is

A triangle is formed by the points A(2,5)B(3,8) and C(x,y). If the centroid of Delta ABC is (3,5) then find the value of 8((1)/(x)-(1)/(y))

(i) A variable plane, which remains at a constant distance '3p' from the origin cuts the co-ordinate axes at A, B, C. Show that the locus of the centroid of the triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (1)/(p^(2)) . (ii) A variable is at a constant distance 'p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of th triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (9)/(p^(2)).

A(3,2) and B(-2,1) are two vertices of a triangle ABC whose centroid G has the coordinates ((5)/(3),-(1)/(3)). Find the coordinates of the third vertex C of the triangle.

If A(1,a),B(a,a^(2)) and C(a^(2),a^(2)) are the vertices of a triangle which are equidistant from the origin,then the centroid of the triangle ABC is at the point

In triangle ABC where,A,B,C are acute, the distances of the orthocentre from the sides are in the proportion