The following set of coordinates most specifically represents which figure? (−5, 6), (−1, 8), (3, 6), (−1, 4) (6 points) Parallelogram Rectangle Rhombus Square

Answer:RhombusStep-by-step explanation:The given points are A(−5, 6), B(−1, 8), C(3, 6), D(−1, 4).We use the distance formula to find the length of AB.[tex]|AB|=\sqrt{(-1--5)^2+(8-6)^2}[/tex][tex]|AB|=\sqrt{16+4}[/tex][tex]|AB|=\sqrt{20}[/tex]The length of AD is [tex]|AD|=\sqrt{(-1--5)^2+(6-4)^2}[/tex][tex]|AD|=\sqrt{16+4}[/tex][tex]|AD|=\sqrt{20}[/tex]The length of BC is:[tex]|BC|=\sqrt{(-1-3)^2+(8-6)^2}[/tex][tex]|BC|=\sqrt{16+4}[/tex][tex]|BC|=\sqrt{20}[/tex]The length of CD is [tex]|CD|=\sqrt{(-1-3)^2+(6-4)^2}[/tex][tex]|CD|=\sqrt{16+4}[/tex][tex]|CD|=\sqrt{20}[/tex]Since all sides are congruent the quadrilateral could be a rhombus or a square.Slope of AB[tex]=\frac{8-6}{-1--5}=\frac{1}{2}[/tex]Slope of BC [tex]=\frac{8-6}{-1-3}=-\frac{1}{2}[/tex]Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be  a square. It is a rhombus