Okay, here we have this;
Considering the provided points, we are going to identify if it's a quadrilateral or not, so we obtain the following:
According to the given points it tells us that a can be any value, so if we take a=2 and plot the points we get the following:
We can see that the four points form a quadrilateral with 90 degree angles, now let's calculate the distances to know what type of quadrilateral it is:
Distance from A to B:
d=√((2-0)^2+(0-0)^2)=√4=2
Distance from B to C:
d=√((2-2)^2+(2-0)^2)=√4=2
Distance from C to D:
d=√((0-2)^2+(2-2)^2)=√4=2
Distance from D to A:
d=√((0-0)^2+(0-2)^2)=√4=2
Finally we get that it is a square because all its angles measure 90 degrees and all its sides are equal.