Answer:
Step-by-step explanation:
Vertices of the given quadrilateral are A(-4, 3), B(2, -1), C(2, -5) and D(-4, -1)
Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of AB = [tex]\frac{3+1}{-4-2}[/tex]
= [tex]-\frac{2}{3}[/tex]
Slope of AD = [tex]\frac{3+1}{-4+4}[/tex]
= Not defined (Parallel to y-axis)
Slope of DC = [tex]\frac{-5+1}{2+4}[/tex]
= [tex]-\frac{2}{3}[/tex]
Slope of BC = [tex]\frac{-1+5}{2-2}[/tex]
= Not defined (Parallel to y-axis)
Slope of AB = slope of DC = [tex]-\frac{2}{3}[/tex]
Slope of BC = slope of AD = Not defined (parallel to y-axis)
As per property of a parallelogram,
"Opposite sides of a parallelogram are parallel and equal in measure"
Therefore, ABCD is a parallelogram.
