Answer
Rhombus
Work Step by Step
Our aim is to apply the distance formula to compute the type of triangle that is given in the picture.
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 all sides of the parallelogram.
$LM= \sqrt {(1-3)^2 + (2-3)^2}=\sqrt 5$ and $NP= \sqrt {(5-3)^2 + (2-1)^2}=5$ 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 all sides of the parallelogram have equal lengths, this means that they are congruent.
Next, we will compute slope of two consecutive sides of the parallelogram.
$m\overline{LM}= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-3}{1-3}=-\dfrac{1}{2}$
We can see that the slopes of the consecutive sides of the parallelogram shows a negative slope.This means that the sides are not perpendicular.
Therefore, the given parallelogram is a rhombus with four congruent sides and whose consecutive sides are not perpendicular.
