Q. The centroid of the triangle formed by joining the mid points of the sides of a triangle with vertices $ (-1,-1),(2,4) $ and $ (-5,-6) $ is
J & K CETJ & K CET 2010Straight Lines
Solution:
Midpoint of $ AB=D\left( \frac{1}{2},\frac{3}{2} \right) $
Midpoint of $ BC=E\left( -\frac{3}{2},-1 \right) $
and mid point of
$ AC=F\left( -3,-\frac{7}{2} \right) $
$ \Delta \,DEF $
is the triangle whose centroid is to be determined.
$ \therefore $ Centroid of $ \Delta \,\,DEF $
is $ \left( \frac{\frac{1}{2}-3-\frac{3}{2}}{3},\frac{\frac{3}{2}-\frac{7}{2}-1}{3} \right) $
$ =\left( \frac{1-6-3}{6},\frac{3-7-2}{6} \right)=\left( -\frac{4}{3},-1 \right) $
