Question

ABC is a triangle whose vertices are A(3,4),B(-2,-1) and C(5,3).If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

Answer 1

Answer:

( 1, 0 )

Step-by-step explanation:

A = ( 3, 4 )      B = ( -2, -1 )       C = ( 5, 3 )

The centroid G is the mean of these, so

G = ( A + B + C ) / 3.

Since BDCG is a parallelogram, we have

D - B = C - G

=> D = B + C - G = ( B + C ) - ( A + B + C ) / 3

        = ( 2B + 2C - A ) / 3

   = ( -4 + 10 - 3, -2 + 6 - 4 ) / 3

   = ( 3, 0 ) / 3

   = ( 1, 0 )