Answer:
ABCD is a RHOMBUS or a SQUARE.
Step-by-step explanation:
The coordinates are A(-6, 6), B(-2, 8), C(0, 4), and D(-4, 2).
By DISTANCE FORMULA:
The length of the segment with coordinates X(a,b) and Y(c,d) is given as:

Now, similarly, the lengths of the segments are:


⇒ The length of the segment AB = √ 20 units


⇒ The length of the segment BC = √ 20 units


⇒ The length of the segment CD= √ 20 units


⇒ The length of the segment AD = √ 20 units


⇒ The length of the diagonal AC = √ 40 units


⇒ The length of the diagonal BD = √ 40 units
Since, here the length of all segments is √ 20 units.
⇒AB = BC = CD = AD = √ 20 units
and Diagonal AC = BD
⇒ ABCD is a RHOMBUS or SQUARE.