Answer:
(-5, -3)
Explanation:
We can use the fact that the diagonals of a parallelogram bisect each other
Let me classify the points as
A (-4, 7)
B (2, -5)
C (3, 5)
Let us assume the 4th vertex is D(x, y) where x and y have to be determined
We will assume that AB is the diagonal of the parallelogram ABCD
The midpoint of a line segment from (x1, y1) to (x2, y2) is given by
(1/2)(x1 + x2, y1 + y2) ie the average of their x and coordinates
If we let O be the midpoint of AB, coordinates of O are
1/2 x (-4 + 2, 7 -5) = 1/2 x ( -2, 2) = (-1, 1)
We know the other diagonal CD must pass through point O and O is also the midpoint of CD
Therefore if coordinates of D are (x, y)
then x-coordinate of O which is -1 should be the average of x coordinate of C and x coordinate of D
==> - 1 = (3 + x)/2
=> -2 = 3 + x
=> -2 - 3 = x
=> -5 = x
=> x = -5
Similarly
1 = (5 + y)/2
=> 2 = 5 + y
=> 2 - 5 = y
=> -3 = y
y = -3
So the coordinate of the fourth vertex D are (-3, -5)
Check the attached graphs for a clearer understanding