Question

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

• A. $\left(-\frac{2}{3},1\right)$
• B. $\left(-\frac{4}{3},-1\right)$
• C. $\left(-\frac{1}{3},\frac{1}{2}\right)$
• D. $\left(-\frac{1}{4},\frac{1}{4}\right)$

Answer 1

Answer: (B)

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 $\left(\frac{\frac{1}{2}-3-\frac{3}{2}}{3},\frac{\frac{3}{2}-\frac{7}{2}-1}{3}\right)$
$=\left(\frac{1-6-3}{6},\frac{3-7-2}{6}\right)=\left(-\frac{4}{3},-1\right)$