the mid points of the sides of a triangle are (3,4) , (4,1) , (2,0).find the coordinates of the vertices of the triangle.

Let A(x ₁ ,y ₁ ) , B(x ₂ ,y ₂ ), C(x ₃ ,y ₃ ) be the vertices of a triangle and D(3,4),E(4,1),F(2,0)be the midpoint of sides AB,BCand CA

Then by midpoint formula,

 (x₁+x₂/2 , y₁+y₂/2)=(3,4)

 x₁+x₂/2 =3

 x₁+x₂₌₆

 (y₁+y₂/2)=4

 y₁+y₂=8

Similarly, use mid point formula again to get 4 more equations. Solve the equations to get the coordinates of A, B, and C