Answer:
The distances between the given points are;
MN = PQ = √41
PN = QM = √26
Step-by-step explanation:
The given coordinates of the vertices of the quadrilateral are;
A(-3, -4), B(3, 0), C(5, 6), D(-7, 2)
The midpoint of AB = The point M
The midpoint of BC = The point N
The midpoint of CD = The point P
The midpoint of DA = The point Q
Therefore;
The coordinates of the point M = ((-3 + 3)/2, (-4 + 0)/2) = (0, -2)
The coordinates of the point N = ((3 + 5)/2, (0 + 6)/2) = (4, 3)
The coordinates of the point P = ((5 + (-7))/2, (6 + 2)/2) = (-1, 4)
The coordinates of the point Q = ((-7 + (-3))/2, (2 + (-4))/2) = (-5, -1)
The formula for the distance, d, between two coordinates is given as follows;

The distance of MN using an online distance between coordinates calculation tool is therefore;

The distance of PQ is given as follows;

Therefore;
MN = PQ = √41
The distance of PN is given as follows;

The distance of QM is given as follows;

PN = QM = √26