Detemine the type of quadrilateral described by vertices r(-3,2) s(-1,6) t (3,5) u(1,1) show all Steps

We have a paralleogram

The slope of the line segment from (1,1) to (3,5)  =  the slope of the line segment from (-3,2) to (-1,6) = 2

Thus, these segments are parallel

And the slope of the line segment from (-1,6) to (3,5) = the slope of the line segment from (-3,2) to (1,1) = -1/4

So these segments are also parallel.

And when two parallel transversals intersect another pair of parallel transversals, the quadrilateral formed has opposite sides of equal length. 

Therefore, we have a parallelogram.....a four-sided figure whose oppsite sides are parallel and equal.

Here's a picture......

 P.S.  - if AB = AD, we would have a rhombus but  AD > AB.....

AD = √20     AB = √17