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Mathematics Question on Straight lines

The centroid of the triangle formed by joining the mid points of the sides of a triangle with vertices (−1,−1),(2,4)(-1,-1),(2,4) and (−5,−6)(-5,-6) is

A

(−23,1)\left( -\frac{2}{3},1 \right)

B

(−43,−1)\left( -\frac{4}{3},-1 \right)

C

(−13,12)\left( -\frac{1}{3},\frac{1}{2} \right)

D

(−14,14)\left( -\frac{1}{4},\frac{1}{4} \right)

Answer

(−43,−1)\left( -\frac{4}{3},-1 \right)

Explanation

Solution

Midpoint of AB=D(12,32)AB=D\left( \frac{1}{2},\frac{3}{2} \right)

Midpoint of BC=E(−32,−1)BC=E\left( -\frac{3}{2},-1 \right)
and mid point of
AC=F(−3,−72)AC=F\left( -3,-\frac{7}{2} \right)
Δ DEF\Delta \,DEF is the triangle whose centroid is to be determined.

∴\therefore Centroid of Δ  DEF\Delta \,\,DEF

is (12−3−323,32−72−13)\left( \frac{\frac{1}{2}-3-\frac{3}{2}}{3},\frac{\frac{3}{2}-\frac{7}{2}-1}{3} \right)

=(1−6−36,3−7−26)=(−43,−1)=\left( \frac{1-6-3}{6},\frac{3-7-2}{6} \right)=\left( -\frac{4}{3},-1 \right)