Question

The three vertices of a parallelogram are (3,4) ,(3,8) and (9,8). Find the fourth vertex

Answer 1

Let ABCD be a parallelogram.
then A ( 3,4), B (3,8) and C (9,8 ). Let the coordinates of D be (x,y)
Since the diagonals of a parallelogram bisect each other
Coordinates of the mid-point of AC = Coordinates of the mid-point of BD
3+9/2 , 4+8/2 = 3+x/2 , 8+y/2
12/2 , 12/2     =3+x/2 , 8+y/2
6 = 3+x/2       , 6 =  8+y/2
12 = 3+x        , 12 = 8+y
12-3 = x         , 12-8 = y
 9 =x               , 4 =y
∴ Coordinates of the fourth vertex are ( 9, 4)

Answer 2

Answer:

9,4 is the correct answer