Question

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)

Answer 1

Answer:

The parallelogram is a rhombus.

Step-by-step explanation:

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

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

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

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

Again, slope of KM = $\frac{-7 - ( - 1)}{- 1 - ( - 3)} = - 3$

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

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