Answer
Rhombus
Work Step by Step
The distance formula is given by the following formula:
$d = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}$
We will compute the lengths of one pair of opposite sides of the parallelogram.
$d_1= \sqrt {(-3-0)^2 + (0-(-3))^2}=\sqrt {18}$ and $d_2= \sqrt {(-3-0)^2 + (0-(-3))^2}=\sqrt {18}$ and $MN= \sqrt {(3-5)^2 + (3-2)^2}=\sqrt 5$and $LP= \sqrt {(1-3)^2 + (2-1)^2}=\sqrt 5$
We can see that the lengths of one pair of opposite sides of the parallelogram have equal lengths, this means that they are congruent.
Next, we will compute slope of any pair of opposite sides of the parallelogram.
$m_1= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-3}{-3-0}=1$ and $m_2= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-3-0}{0-3}=1$
We can see that the slopes of the opposite sides of the parallelogram are same, this means that the lines are parallel.
Therefore, the given parallelogram is a rhombus with four congruent sides.
