Question

In triangle ABC, base BC and area of triangle ${}^{\prime }{\Delta }^{\prime }$ 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 to side BC

Answer 1

The correct option is A

parallel to side BC

$\Delta =\frac{1}{2}\left(BC\right)h,\text{where 'h' is the distance of vertex 'A' from side BC.}{\Delta }_{GBC}=\frac{\Delta }{3}=\frac{\left(BC\right)h}{6},\text{where 'G' is centroid.}\Rightarrow h=\frac{2\Delta }{\left(BC\right)}=\text{constant}\text{Thus distance of vertex 'A' from side is fixed. This implies that distance of centroid from side BC will be fixed, hence locus of 'G' will be a line parallel to BC.}$