Answer
$$m_{AD}=m_{BC}$$ $$m_{DC}=m_{AB}$$
$$m_{AD}m_{DC}=-1$$ $$m_{AB}m_{BC}=-1$$
Work Step by Step
We know, that each side of a rectangle has the same slope as its opposite side. Also, the sides connecting vertices are perpendicular (It means, that product of their slopes is $-1$).
Above is visual representation of the points provided. We have to prove, that $m_{AD}=m_{BC}$ and $m_{DC}=m_{AB}$.
To check whether or not its rectangle (each angle is $90°$) we also have to prove, that $m_{AD}m_{DC}=-1$ and $m_{AB}m_{BC}=-1$
$m_{AD}=\frac{6-1}{0-1}=\frac{5}{-1}=-5$
$m_{BC}=\frac{8-3}{10-11}=\frac{5}{-1}=-5$ $$m_{AD}=m_{BC}$$
$m_{DC}=\frac{8-6}{10-0}=\frac{2}{10}=\frac{1}{5}$
$m_{AB}=\frac{3-1}{11-1}=\frac{2}{10}=\frac{1}{5}$ $$m_{DC}=m_{AB}$$
We have found, that sides of this figure are parallel.
$$m_{AD}m_{DC}=-5\times \frac{1}{5}=-1$$ $$m_{AB}m_{BC}=\frac{1}{5}\times (-5)=-1$$
