Answer:
Yes, the given parallelogram is a rectangle.
Step-by-step explanation:
The vertices of parallelogram are J(-5,0), K(1,4), L(3,1) and M(-3,-3).
The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]JK=\frac{4-0}{1-(-5)}=\frac{4}{6}=\frac{2}{3}[/tex]
[tex]KL=\frac{1-4}{3-1}=\frac{-3}{2}[/tex]
[tex]LM=\frac{-3-1}{-3-3}=\frac{-4}{-6}=\frac{2}{3}[/tex]
[tex]JM=\frac{-3-0}{-3-(-5)}=\frac{-3}{2}[/tex]
The slopes of opposites sides are same it means they are parallel to each other.
The product of slopes of two consecutive sides is
[tex]\frac{2}{3}\times \frac{-3}{2}=-1[/tex]
Since the product of slopes of two consecutive sides is -1, therefore the consecutive sides are perpendicular to each other.
Yes, the given parallelogram is a rectangle.
