Question

in triangle abc A=( 5,8) ,D is the midpoint of side BC =( 2, - 1)
find the centroid of triangle ABC ​

Answer 1

Coordinate of centroid of triangle is (3,2)

Explanation:

1. Given data

  Coordinate of point A $\mathbf{(x_{1},y_{1})=(5,8)}$

  Where D is mid point of BC. So AD is median of triangle.

  Coordinate of point D $\mathbf{(x_{2},y_{2})=(2,-1)}$

  Let

  Coordinate of centroid G $\mathbf{(x,y)}$

2. Where D is mid point of BC. So AD is median of triangle.

   We know that centroid of triangle bisect the median 2:1.

   Means

   Point G bisect A and D in 2:1

3. So coordinate of G can be found by formula

   $\mathbf{(x.y)=\left ( \frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n} \right )}$  

   here

   m=2 and n=1

  $\mathbf{(x.y)=\left ( \frac{2\times 2+1\times 5}{2+1},\frac{2\times (-1)+1\times 8}{2+1} \right )}$

  On solving

  (x,y)= (3,2)