If three vertices of a parallelogram in the plane are (-5,3), (5,2) and (7,-8), determine all the possible

If three vertices of a parallelogram in the plane are (-5,3), (5,2) and (7,-8), determine all the possible coordinates of the fourth vertex.

please help, thanks :)

In this case, there are actually 3 possibilities of the fourth vertex. Try plotting your points first, and you will see that 3 answers actually work.

We'll start with the three points we have. A(-5,3), B(5,2) and C(7,-8).

Let's create line segments using the points we got.
BA = B - A = (5,2) - (-5,3) = (10, -1)
AC = A - C = (-5,3) - (7,-8) = (-12, 11)
CB = C - B = (7,-8) - (5,2) = (2, -10)

Possibility #1: Add line segment CB to point A.
(2, -10) + (-5,3) = (-3, -7) << Fourth Vertex

Possibility #2: Add line segment BA to point C.
(10, -1) + (7,-8) = (17, -9) << Fourth Vertex

Possibility #3: Add line segment AC to point B.
(-12, 11) + (5,2) = (-7, 13) << Fourth Vertex

Coordinates: (-3,-7), (17,-9) and (-7,13)

(-3, 8)