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The coordinates of the vertices of quadrilateral JKLM are J(−3, 2) , K(3, 5) , L(9, −1) , and M(2, −3) .



Which statement correctly describes whether quadrilateral JKLM is a rhombus?


Quadrilateral JKLM is not a rhombus because opposite sides are parallel but the four sides do not all have the same length.

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

Quadrilateral JKLM is a rhombus because opposite sides are parallel and all four sides have the same length.

Quadrilateral JKLM is not a rhombus because there is only one pair of opposite sides that are parallel.

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SaniShahbaz

Answer:

We conclude that Quadrilateral JKLM is not a rhombus because there is only one pair of opposite sides that are parallel.

Step-by-step explanation:

The coordinates of the vertices of quadrilateral JKLM are:

  • J(−3, 2)
  • K(3, 5)
  • L(9, −1)
  • M(2, −3)

As

[tex]JK\:slope\:=\:\frac{\left(2-5\right)}{\left(-3-3\right)}=\frac{-3}{-6}=\frac{1}{2}[/tex]

[tex]ML\:slope\:=\:\frac{\left(-3+1\right)}{\left(2-9\right)}=\frac{-2}{-7}=\frac{2}{7}[/tex]

[tex]JM\:slope\:=\:\frac{\left(2+3\right)}{\left(-3-2\right)}=\frac{5}{-5}=-1[/tex]

[tex]KL\:slope\:=\:\frac{\left(5+1\right)}{\left(-3-9\right)}=\frac{6}{-6}=-1[/tex]

As parallel lines have same slope

So,

  • JM and KL have same slope
  • JK and ML do not have same slope

Therefore, from the above discussion, we conclude that Quadrilateral JKLM is not a rhombus because there is only one pair of opposite sides that are parallel.

Keywords: rhombus, quadrilateral, slope

Learn more about rhombus from brainly.com/question/1206531

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