The x,y,z coordinates of each vertex of a triangle are in geometric progression .The x and y coordinates of the centroid of the triangle are $$1$$ and $$2$$ respectively. The distance of the centroid from the origin is.

Question

The x,y,z coordinates of each vertex of a triangle are in geometric progression  .The x and y coordinates of the centroid of the triangle are $$1$$ and $$2$$ respectively. The distance of the centroid from the origin is.

Infinity Learn · Accepted Answer

Given x,y,z coordinates of each vertex of a triangle are in geometric progressionand the centroid of the triangle is $$x1+x2+x33$$,$$y1+y2+y33$$,$$z1+z2+z33=(1$$,$$2$$,$$k)it$$ implies that $$x1+x2+x3=3$$,$$y1+y2+y3=6suppose$$ that r is common ratio of geometric progression, $$r(x1+x2+x3)=6$$⇒$$r(3)=6$$⇒$$r=2Hence$$, $$z1+z2+z3=r2(x1+x2+x3)=4(3)=12The$$ centroid of the triangle is $$1$$,$$2$$,$$4The$$ distance of the centroid from origin is $$1+4+16=21$$

The $x, y, z$ coordinates of each vertex of a triangle are in geometric progression .The $x$ and $y$ coordinates of the centroid of the triangle are 1 and 2 respectively. The distance of the centroid from the origin is.

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The x,y,z coordinates of each vertex of a triangle are in geometric progression .The x and y coordinates of the centroid of the triangle are 1 and 2 respectively. The distance of the centroid from the origin is.

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The $x, y, z$ coordinates of each vertex of a triangle are in geometric progression .The $x$ and $y$ coordinates of the centroid of the triangle are 1 and 2 respectively. The distance of the centroid from the origin is.