Step-by-step explanation:
let's consider BA and CD as one pair of sides, and CB and DA as the second pair of sides.
the slope BA = -1
as x changes +4 (from 0 to 4), and y changes -4 (from 4 to 0).
the slope of CD = -1
as x changes +4 (from -4 to 0) and y changes -4 (from 0 to -4).
so, both lines are indeed parallel.
the slope CB = +1
as x changes +4 (from -4 to 0) and y changes +4 (from 0 to 4)
the slope of DA = +1
as x changes +4 (from 0 to 4) and y changes +4 (from -4 to 0)
so, these 2 lines are also parallel to each other and perpendicular to the first 2 lines (x and y in the slope ratio upside-down, and the sign is flipped).
therefore, we have only 90° angles here.
and the sums of the x and y coordinate differences are the same for every side, so all sides are equally long.
therefore, this is a square.
and with that it is automatically also a rectangle and a rhombus.
