A triangle ABC is placed so that the $$mid-points$$ of the sides are on the x,y,z axes. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively α,β,γ .Coordinates of the centroid of the triangle ABC are

Question

A triangle ABC is placed so that the $$mid-points$$ of the sides are on the x,y,z axes. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively α,β,γ .Coordinates of the centroid of the triangle ABC are

Infinity Learn · Accepted Answer

Let D,E,F be the midpoints of the sides BC, CA and AB respectively.Then $$D=$$α,$$0$$,$$0$$, $$E=0$$,β,$$0$$ and $$F=0$$,$$0$$,γWe know that centroid of the triangle is same as centroid of the triangle formed with midpoints D,E,F.⇒$$Centroid=G=$$α$$3$$,β$$3$$,γ$$3$$

$A triangle ABC is placed so that the mid-points of the sides are on the x,y,z axes. Lengths of the intercepts made by$
$the plane containing the triangle on these axes are respectively α, β, γ . Coordinates of the centroid of the triangle ABC are$

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A triangle ABC is placed so that the mid-points of the sides are on the x,y,z axes. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively α,β,γ .Coordinates of the centroid of the triangle ABC are

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$A triangle ABC is placed so that the mid-points of the sides are on the x,y,z axes. Lengths of the intercepts made by$
$the plane containing the triangle on these axes are respectively α, β, γ . Coordinates of the centroid of the triangle ABC are$