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Dima020 [189]
1 year ago
13

The coordinates of the vertices of quadrilateral ABCD are A(−6, 3) , B(−1, 5) , C(3, 1) , and D(−2, −2) . Which statement correc

tly describes whether quadrilateral ABCD is a rhombus?
Mathematics
1 answer:
Pavlova-9 [17]1 year ago
8 0

Answer:

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

Complete question:

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.

Step-by-step 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 (x_{1},y_{1}), (x_{2},y_{2})  to be parallel to (x_{3},y_{3}),  (x_{4},y_{4}) is matching slopes;

\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{y_{4}-y_{3}}{x_{4}-x_{3}} \\(y_{2}-y_{1}) \cdot (x_{4}-x_{3}) =(y_{4}-y_{3}) \cdot (x_{2}-x_{1})---->1

So, we have to check that AB || CD and AD || BC

First check AB || CD

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

substitute in [1],

(5-3) \cdot (-2-3) = (-2-1) \cdot (-1-(-6))2 \cdot -5 = -3 \cdot 5

-10 ≠ -15

Similarly,

check AD || BC

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

Substitute in [1], we have

(-2-3) \cdot (3-(-1)) = (1-5) \cdot (-2-(-6))-5 \cdot 4 = -4 \cdot 4

-20 ≠ -16.

Both pairs of sides are not parallel,

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

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