The coordinates of the vertices of quadrilateral abcd are a(−6, 3) , b(−1, 5) , c(3, 1) , and d(−2, −2) . which statement correctly describes whether quadrilateral abcd is a rhombus? a. quadrilateral abcd is not a rhombus because opposite sides are parallel but the four sides do not all have the same length. b. quadrilateral abcd is a rhombus because opposite sides are parallel and all four sides have the same length. c. quadrilateral abcd is not a rhombus because there are no pairs of parallel sides. d. quadrilateral abcd is not a rhombus because there is only one pair of opposite sides that are parallel. 25 points for the answer

The answer is c.

Step-by-step explanation:

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Option C is correct.

Explanation:

Rhombus states that a parallelogram with four equal sides and sometimes one with no right angle.

Given: The coordinate of the vertices of quadrilateral ABCD are A(−6, 3) , B(−1, 5) , C(3, 1) , and D(−2, −2) .

The condition for the segment , to be parallel to ,   is matching slopes;

or

    ....[1]

So, we have to check that and

First check

A(−6, 3) , B(−1, 5) , C(3, 1) , and D(−2, −2)

substitute in [1],

-10 ≠ -15

Similarly,

check

A(−6, 3) , D(−2, −2) , B(−1, 5) and C(3, 1)

Substitute in [1], we have

-20 ≠ -16.

Both pairs of sides are not parallel,

therefore, Quadrilateral ABCD is not a rhombus because there are no pairs of parallel sides.