Question

In triangle $ABC$, base $BC$ and area of triangle $△$ are fixed. Locus of the centroid of triangle $ABC$ is a straight line that is:

• A. parallel to side $BC$
• B. right bisector of side $BC$
• C. right angle of $BC$
• D. inclined at an angle ${\sin }^{-1}\left(\frac{\sqrt{\Delta }}{BC}\right)$

Answer 1

The correct option is A parallel to side $BC$

$\Delta =\frac{1}{2}h\left(BC\right)⟹h=\frac{2\Delta }{BC}⟹h$ is fixed

As $h$ and $BC$ are fixed $,A$ moves in a straight line parallel to $BC$ to keep $h$ constant

As $A$ moves in a straight line ,$G$ also moves in a straight line parallel to $BC(\because$ $BC$ is constant$)$