Answer:
The correct option is C.
Step-by-step explanation:
The vertices of ABCD are A(2,-3), B(8,-6), C(14,-3), and D(8,0).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of sides are
[tex]AB=\sqrt{(8-2)^2+(-6+3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
[tex]BC=\sqrt{(14-8)^2+(-3+6)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
[tex]CD=\sqrt{(8-14)^2+(0-3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
[tex]AD=\sqrt{(8-2)^2+(0+3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
Since length of all sides are equation therefore the given parallelogram cannot be a rectangle.
Slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of AB is
[tex]m_1=\frac{-6-(-3)}{8-2}=\frac{-3}{6}=\frac{-1}{2}[/tex]
Slope of BC is
[tex]m_2=\frac{-3-(-6)}{14-8}=\frac{3}{6}=\frac{1}{2}[/tex]
Since the slopes of two consecutive sides are not opposite reciprocals, therefore the given parallelogram is a rhombus. Option C is correct.
