Question 719101
{{{A=-2+i}}}
{{{B=-3+5i}}}
{{{C=1+14i}}}
{{{D=2+10i}}}
{{{B-A=-3+5i-(-2+i)=-3+5i+2-i=-1+4i}}} represents side AB
{{{C-D=1+14i-(2+10i)=1+14i-2-10i=-1+4i}}} represents side DC
As they are the same, it means that the sides are parallel and congruent, which means ABCD is a parallelogram.
{{{drawing(400,400,-9,7,-1,15,
grid(1),
red(arrow(-2,1,-3,5)),red(arrow(2,10,1,14)),
blue(line(-3,5,1,14)),blue(line(-2,1,2,10))
)}}}