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

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1 Answer

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.