Question

If two vertices of a parallelogram are (3,2),(-1,0) and the diagonals cut at (2,-5). Find the other vertices of the parallelogram

Answer 1

Answer:

C(5,-10) & D(1,-12)

Step-by-step explanation:

Let A(3,2), B(-1,0) & E(2,-5)

The diagonals of a parallelogram bisect each other

So,

Using mid-point formula

(for line BC)

E(2,-5) = [-1+x/2,0+y/2]

2=-1+x/2 & -5=y/2

4=-1+x & -10=y

x=5 & y=-10

Therefore, coordinate C is C(5,-10).

(for line AD)

E(2,-5) = [3+x/2,2+y/2]

2=3+x/2 & -5=2+y/2

4=3+x & -10=2+y

x=1, y=-12

Therefore, coordinate D is D(1,-12).