Question

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Answer 1

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

$JK\:slope\:=\:\frac{\left(2-5\right)}{\left(-3-3\right)}=\frac{-3}{-6}=\frac{1}{2}$

$ML\:slope\:=\:\frac{\left(-3+1\right)}{\left(2-9\right)}=\frac{-2}{-7}=\frac{2}{7}$

$JM\:slope\:=\:\frac{\left(2+3\right)}{\left(-3-2\right)}=\frac{5}{-5}=-1$

$KL\:slope\:=\:\frac{\left(5+1\right)}{\left(-3-9\right)}=\frac{6}{-6}=-1$

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

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