Question

which are the coordinates of the vertices of a parrellogram.

Answer 1

In order to have a parallelogram, the opposite sides need to be parallel, that is, they need to have the same slope.

The slope between two points can be calculated using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

So, for option A, we have:

$\begin{gathered} m_1=\frac{3-2}{-1-(-3)}=\frac{1}{2} \\ m_2=\frac{2-3}{2-(-1)}=-\frac{1}{3} \\ m_3=\frac{1-2}{0-2}=\frac{1}{2} \\ m_4=\frac{2-1}{-3-0}=-\frac{1}{3} \end{gathered}$

The slopes m1 and m3 are equal and the slopes m2 and m4 are also equal, so we have a two pairs of opposite parallel sides, therefore the correct option is A.