Question 669221
<pre>
{{{drawing(400,5000/17,-3,14,-3,9.5,

line(-3,0,14,0), line(0,-3,0,9.5), locate(14,0,x),locate(.2,9.5,y),
rectangle(0,0,11,6.5),
locate(0+.2,0,"A(0,0)"),locate(11+.2,0,"B(a,0)"),locate(11+.2,6.5,"C(a,b)"),
locate(0+.2,6.5,"D(0,b)") 



 )}}}

The midpoint of AB is E({{{a/2}}},0),
The midpoint of AB is F({{{a/2}}},{{{b/2}}}),

{{{drawing(400,5000/17,-3,14,-3,9.5,
locate(5,0,E(a/2,0)), circle(5.5,0,.15),
locate(11.3,3.7,F(a,b/2)), circle(11,3.25,.15),
line(-3,0,14,0), line(0,-3,0,9.5), locate(14,0,x),locate(.2,9.5,y),
rectangle(0,0,11,6.5),
locate(0+.2,0,"A(0,0)"),locate(11+.2,0,"B(a,0)"),locate(11+.2,6.5,"C(a,b)"),
locate(0+.2,6.5,"D(0,b)") ,
locate(5,8.5,G(a/2,b)), circle(5.5,6.5,.15),
locate(-3,3.7,H(a,b/2)), circle(0,3.25,.15),
green(line(0,3.25,5.5,0), line(5.5,0,11,3.25), line(11,3.25,5.5,6.5),
line(5.5,6.5,0,3.25))




 )}}}

Using the distance formula, which is:

d = {{{sqrt((x[2]-x[1])^2+(y[2]-y[1])^2)}}}

EF = {{{sqrt((a-a/2)^2+(b/2-0)^2)}}} = {{{sqrt((a/2)^2+(b/2)^2)}}}



FG = {{{sqrt((a/2-a)^2+(b-b/2)^2)}}} = {{{sqrt((-a/2)^2+(b/2)^2)}}} = {{{sqrt((a/2)^2+(b/2)^2)}}}

GH = {{{sqrt((a-a/2)^2+(b/2-b))^2}}} = {{{sqrt((-a/2)^2+(b/2)^2)}}} = {{{sqrt((a/2)^2+(b/2)^2)}}}

HE = {{{sqrt((a/2-a)^2+(0-b/2)^2)}}} = {{{sqrt((a/2)^2+(-b/2)^2)}}} = {{{sqrt((a/2)^2+(b/2)^2)}}}

All four sides of EFGH are equal to {{{sqrt((a/2)^2+(b/2)^2)}}} so EFGH is a rhombus.

Edwin</pre>