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Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Select the most specific name that applies. J(−8, −6), K(−3, −1), L(4, −2), and M(−1, −7)

Respuesta :

Answer:

The parallelogram is a rhombus.

Step-by-step explanation:

Length of diagonal JL is = [tex]\sqrt{(- 8 - 4)^{2} + (- 2 - ( - 6))^{2} } = \sqrt{160}[/tex] units.

And the length of diagonal KM is = [tex]\sqrt{(- 1 - (- 3))^{2} + (- 7 - ( - 1))^{2} } = \sqrt{40}[/tex] units.

So, JL ≠ KM so, the parallelogram is neither rectangle nor a square.

Now, Slope of line JL = [tex]\frac{-2 - ( - 6)}{4 - (- 8)} =  \frac{1}{3}[/tex]

Again, slope of KM = [tex]\frac{-7 - ( - 1)}{- 1 - ( - 3)} = - 3[/tex]

Therefore, the product of slope of JL and KM is - 1 and hence, JL ⊥ KM

And therefore, the parallelogram is a rhombus. (Answer)

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