Question

Three vertices of a rectangle are given. Find the coordinates of the fourth vertex.

Answer 1

Start with two vertex points from one side of the rectangle:
(4, 0) and (2, -3).
Subtract the X coordinates:  4 - 2 = 2
Subtract the Y coordinates:  0 - -3 = 3
Now, start with the third vertex point that is given:
(-2,4).
The differences for the X & Y coordinates between the third vertex point and the fourth vertex point will be the same as the differences between the 1st and 2nd points, so start with the 3rd point X coordinate and subtract 2 from it to get the X coordinate for the fourth point:
-2 - 2 = -4.
Then, take the 3rd point Y coordinate and subtract 4 to get the Y coordinate for the fourth point:
4 - 3 = 1
So, your fourth vertex point is (-4, 1).
See the attached picture.
This works because each of the two sets of sides of a rectangle are parallel to each other.