Question

The three verticess of a Parallelogram (3,4), (3,8), (9,8). Find the fourth vertex.

Answer 1

hey here is your answer

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)

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