Question 805403
AB is parallel to CD and BC is parallel to AD.
There are no perpendicular lines.
ABCD is a parallelogram, but not a rectangle.
 
Parallel lines have the same slope. Perpendicular lines have slopes whose product is {{{-1}}}.
slope of AB = {{{(4-2)/(3-0)=2/3}}} and slope of DC = {{{(7-5)/(3-0)=2/(2+1)=2/3}}}
Both slopes are the same, so AB is parallel to DC 
slope of BC = {{{(7-4)/(2-3)=3/(-1)=-3}}} and slope of DA = {{{(5-2)/(-1-0)=3/(-1)=-3}}}
Both slopes are the same, so BC is parallel to DA.
 
The product of the slopes {{{2/3}}} and {{{-3}}} is
{{{(2/3)(-3)=-2<>-1}}} so there are no perpendicular lines in ABCD.
 
From the drawing (see below) I can tell that it is not a rhombus, because the sides have different length, so diagonals AC and BD are not perpendicular.
AB and CD are {{{sqrt(13)}}} units long.
BC and DA are {{{sqrt(10)}}} units long

{{{drawing(300,300,-4,6,-1,9,
grid(1),
blue(line(0,2,3,4)),blue(line(2,7,3,4)),
blue(line(2,7,-1,5)),blue(line(0,2,-1,5)),
green(line(0,2,2,7)),green(line(3,4,-1,5)),
locate(0.1,2,A),locate(3.1,4,B),
locate(2.1,7.5,C),locate(-1.3,5.5,D)
)}}}