Question

Three consecutive vertices of a parallelogram ABCD are A(S, 5), B(-7, -5) and C(-5, 5). Find the coordinates of the fourth vertex D. 

Answer 1

we know that in a parallelogram diagonals bisect each other 

∴ midpoint of AC = midpoint of BD

`"O" ((8 - 5)/2 , (5 + 5)/2) = "O"(("x" - 7)/2 , ("y" - 5)/2)`

`(8 - 5)/2 = ("x" - 7)/2 , (5 + 5)/2 = ("y" - 5)/2`

`3/2 = ("x" - 7)/2 , 10 = "y" - 5`

x = 10 , y = 15

Coordinates of fourth vertex D are (10 , 15)