Question 1094441
Points {{{S(-2,-1)}}} and {{{T(5,-1)}}} define a horizontal segment ST,
with a length of {{{5-(-2)=7}}} units.
{{{drawing(480,300,-7,9,-6,4,grid(1),
red(triangle(1,3,-2,-1,5,-1)),locate(1.1,3.5,R),
locate(-2.3,-1,S),locate(5.1,-1,T)
)}
Segment TS must be either a side of the parallelogram,
or one of its diagonals.
If it is a side,
the fourth vertex must be {{{7}}} units to the left of {{{R(1,3)}}} , at U,
or {{{7}}} units to the right of {{{R(1,3)}}} , at V.
with an x-coordinate of either{{{x=1-7=-6}}} or {{{x=1+7=8}}} ,
and of course the same {{{y=3}}} as point R.
So, {{{highlight(U(-6,3))}}} and {{{highlight(V(8,3))}}} are two of the possible locations of the fourth vertex.
Those two options give you parallelograms SURT and SRVT, shown below.
{{{drawing(480,300,-7,9,-6,4,grid(1),
red(triangle(1,3,-2,-1,5,-1)),locate(1.1,3.5,R),
locate(-2.3,-1,S),locate(5.1,-1,T),
red(triangle(1,3,-2,-1,-6,3)),locate(-6.3,3.5,U)
)}}} and {{{drawing(480,300,-7,9,-6,4,grid(1),
red(triangle(1,3,-2,-1,5,-1)),locate(1.1,3.5,R),
locate(-2.3,-1,S),locate(5.1,-1,T),
red(triangle(1,3,5,-1,8,3)),locate(8.1,3.5,V)
)}}}

If ST is a diagonal, then RT and RS are sides,
R is above diagonal ST, and fourth vertex W is below the diagonal
with SW parallel to RT,
SW slanting down from {{{S(-2,-1)}}} , just as RT slants down from R,
going {{{y[R]-y[T]=3-(-1)=4}}} units down,
and {{{x[T]-x[R]=5-1=4}}} units to the right.
That gives us {{{y[W]=y[S]-4=-1-4=-5}}} ,
and {{{x[W]=x[S]+4=-2+4=2}}} ,
and puts the fourth vertex at {{{highlight(W(2,-5))}}} .
With W, you form parallelogram SWTR, shown below.
{{{drawing(480,300,-7,9,-6,4,grid(1),
red(triangle(1,3,-2,-1,5,-1)),locate(1.1,3.5,R),
locate(-2.3,-1,S),locate(5.1,-1,T),
red(triangle(-2,-1,5,-1,2,-5)),locate(2.1,-5,W)
)}}}