Answer:
Rectangle
Step-by-step explanation:
The given quadrilateral has coordinates at: P (3,7), Q (-1,7), R (3, -1) and S (-1, -1).
The length of PQ is given by:
[tex]|PQ|=|3--1|=|4|=4[/tex]
The length of QS is [tex]|QS|=|7--1|=|8|=8[/tex]
The length of RS is [tex]|RS|=|3--1|=|4|=4[/tex]
The length of PR is [tex]|PR|=|7--1|=|8|=8[/tex]
The slope of PQ is [tex]\frac{7-7}{3--1}=0[/tex]
The slope of QS is [tex]\frac{-1-7}{-1+1}= \infty[/tex]
The slope of RS [tex]\frac{-1--1}{-1-3} =0[/tex]
The slope of PR is [tex]\frac{-1-7}{3-3}=\infty[/tex]
The  quadrilateral has pair of parallel sides equal and adjacent sides perpendicular.
This is a rectangle
