Question

What is the 4th coordinate for the given coordinates (-1,2),(3,6), and (-2,4) to become a parallelogram?

Answer 1

`H(0, 0)` and `G(-5, -2)`

Explanation:

Given intersection of the diagonals `D(-1, 2)=D(x_D, y_D)`
All that is needed is to solve for the endpoints of the diagonals.
The formula

`x_D=(x_E+x_G)/2`

`-1=(3+x_G)/2`

`-2=3+x_G`

`x_G=-5`

Also

`y_D=(y_E+y_G)/2`

`2=(6+y_G)/2`

`4=6+y_G`

`y_G=-2`

and therefore `G(-5, -2)`

For the other point `H(x_H, y_H)`

`x_D=(x_F+x_H)/2`

`-1=(-2+x_H)/2`

`-2=-2+x_H`

`x_H=0`

Also

`y_D=(y_F+y_H)/2`

`2=(4+y_H)/2`

`4=4+y_H`

`y_H=0`

and therefore `H(0, 0)`

God bless.....I hope the explanation is useful.