question_answer

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)  \[\left( -\frac{1}{4},\frac{1}{4} \right)\]

Correct Answer: B

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