Question

(2, 0) is centroid of ABC, if (1, 3) is mid point of BC, then A =

Answer 1

Answer:  A (4,-6)

Step-by-step explanation:

GIVEN THAT [2,0] is the centroid of the triangle.

CASE 1 :

Centroid of the triangle ABC =  G{(x1+x2+x3)/3, (y1+y2+y3)/3}

So, (2,0)={(x1+x2+x3/3),(y1+y2+y3/3)}

     2=x1+x2+x3/3  ,  0= y1+y2+y3/3

       6=x1+x2+x3     ,   0=y1+y2+y3  

       6=x1+x2+x3 ⇒ (i)

       0=y1+y2+y3 ⇒ (ii)

 CASE 2 :

so,Mid point of BC = { x1+x2/2 , y1+y2/2 }

                       (1,3) = { x1+x2/2 , y1+y2/2 }

                         1=x1+x2/2  , 3=y1+y2/2

                          2=x1+x2    , 6= y1+y2  

 by substituting x1+x2 =2 and y1+y2 =6  in equation (i) and (ii)

   you  get  6=2+x3  then x3=4

                    0=6+y3  then y3=-6