Question

ABC is a triangle whose vertices are a( 3, 4 )b -2, - 1 and C (5,3).If G isthe centroid and BDCGis a parallelogram then find the coordinates of the vertex d

Answer 1

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

centroid of ABC = $\left[\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right]$

= [(3 - 2 + 5)/3, (4 - 1 + 3)/3 ]

= [6/3 , 6/3 ] = (2, 2)

again, question said " BDCG is a parallelogram "

so, midpoint of diagonal BD = midpoint of diagonal CG

let D = (x, y)

then, midpoint of BD = [(-2+x)/2, (-1+y)/2 ]

midpoint of CG = [(5+2)/2,(3 + 2)/2 ] = (7/2, 5/2)

hence, [(-2+x)/2, (-1+y)/2] = (7/2, 5/2)

(-2+x)/2 = 7/2 => x = 9

(-1+y)/2 = 5/2 => y = 6


hence, D (9,6)