## Elementary Geometry for College Students (7th Edition)

We name the sides of the rhombus: $(0,0) ; (2b,2c); (2a+2b, 2c); (2a,0)$ Thus, the midpoints are: $(b,c); (a+2b, 2c); (2a+b,c); (a,0)$ Plugging these into the distance formula, we find: $s_1 = \sqrt{c^2 +(b-a)^2}$ $s_2 = \sqrt{c^2 +(-b-a)^2}$ $s_3 = \sqrt{c^2 +(-b-a)^2}$ $s_4 = \sqrt{c^2 +(b-a)^2}$ Since opposite sides are congruent and the angles are 90 degrees, it follows that the shape is a rectangle.