Question

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 1

Answer:

Rhombus

Step-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.

$|AB|=\sqrt{(-1--5)^2+(8-6)^2}$

$|AB|=\sqrt{16+4}$

$|AB|=\sqrt{20}$

The length of AD is

$|AD|=\sqrt{(-1--5)^2+(6-4)^2}$

$|AD|=\sqrt{16+4}$

$|AD|=\sqrt{20}$

The length of BC is:

$|BC|=\sqrt{(-1-3)^2+(8-6)^2}$

$|BC|=\sqrt{16+4}$

$|BC|=\sqrt{20}$

The length of CD is

$|CD|=\sqrt{(-1-3)^2+(6-4)^2}$

$|CD|=\sqrt{16+4}$

$|CD|=\sqrt{20}$

Since all sides are congruent the quadrilateral could be a rhombus or a square.

Slope of AB$=\frac{8-6}{-1--5}=\frac{1}{2}$

Slope of BC $=\frac{8-6}{-1-3}=-\frac{1}{2}$

Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be  a square. It is a rhombus

Answer 2

Answer:

answer is Rhombus

Step-by-step explanation: