we have that
A(-2,1), B(1,5), C(4,4), D(1,0)
using a graph tool
see the attached figure
we know that
A parallelogram is a simple quadrilateral with opposite sides parallel and equal in length
therefore
let's calculate the slope and distance of each side and compare them
side AB
slope m=(y2-y1)/(x2-x1)------> m=(5-1)/(1+2)----> m=4/3
distance AB=√4²+3³-------> dAB=5 units
side CD
slope m=(y2-y1)/(x2-x1)------> m=(0-4)/(1-4)----> m=4/3
distance CD=√4²+3³-------> dCD=5 units
side BC
slope m=(y2-y1)/(x2-x1)------> m=(4-5)/(4-1)----> m=-1/3
distance BC=√1²+3³-------> dBC=√10 units
side AD
slope m=(y2-y1)/(x2-x1)------> m=(0-1)/(1+2)----> m=-1/3
distance AD=√1²+3³-------> dAD=√10 units
(side BC and side AD are parallel) and (side BC=side AD)
and
(side AB and side CD are parallel) and (side AB=side CD)
therefore
the answer is
Yes, it is a parallelogram