=======================================================
Explanation:
Use the slope formula to find the slope of the line through A(-6,-1) and B(-5,2)
[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-5,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - (-1)}{-5 - (-6)}\\\\m = \frac{2 + 1}{-5 + 6}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]
The slope of segment AB is 3.
-------------
Repeat these set of steps for segment CD
C = (-1,-5)
D = (0,-2)
[tex](x_1,y_1) = (-1,-5) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-5)}{0 - (-1)}\\\\m = \frac{-2 + 5}{0 + 1}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]
The slope of segment CD is also 3
Parallel lines have equal slopes, but different y intercepts.
Since AB and CD have the same slope of 3, this shows AB is parallel to CD.
--------------
Now find the slope of segment BD
B = (-5,2)
D = (0,-2)
[tex](x_1,y_1) = (-5,2) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 2}{0 - (-5)}\\\\m = \frac{-2 - 2}{0 + 5}\\\\m = -\frac{4}{5}\\\\[/tex]
Segment BD has a slope of -4/5
--------------
Lastly, compute the slope of segment AC
A = (-6,-1)
C = (-1,-5)
[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-1,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - (-1)}{-1 - (-6)}\\\\m = \frac{-5 + 1}{-1 + 6}\\\\m = -\frac{4}{5}\\\\[/tex]
Segment AC has a slope of -4/5
Both segments BD and AC have the same slope of -4/5.
Therefore, segments BD and AC are parallel
----------------
We have two pairs of opposite parallel sides. Ultimately figure ABDC is a parallelogram
See the diagram below.
