Let the midpoints of the sides RS, ST, TU and UR be M, N, O and P. These midpoints have the average of the endpoints: M(-3,2.5), N(-1.5,1), O(-4,-1.5), P(-5.5,0). If this is a rectangle, we can compare the slopes of MN and OP:
Slope of MN: (2.5-1)/(-3+1.5)=1.5/-1.5=-1; slope of OP=(-1.5-0)/(-4+5.5)=-1.5/1.5=-1. Therefore MN and OP are parallel.
Now the slopes of NO and PM:
Slope of NO: (-1.5+4)/(1+1.5)=2.5/2.5=1; slope of PM: (-5.5+3)/(0-2.5)=-2.5/-2.5=1, so NO and PM are parallel and since the product of the slopes is -1×1=-1 the angle between the two pairs of sides is 90° so we have parallel sides and perpendicularity which is the definition of a rectangle. MNOP is a rectangle.