Polygon

AB and CD are opposite sides, and BC and AC are opposite, we can immediately determine whether it is a trapezoid or not, by determining their lengths.

AB ~ 6.325

CD ~ 7.21

That means it is a trapezoid. But don't trust me, i haven't done geometry in years.

I suggest using desmos graphing calculator to check your answer

It's definitely a quadrilateral....but....it could be something else, too

A(1,1) , B(7,3) , C(1,12) , D (-5,8)

Let's get the lengths of  all 4 sides

AB  = sqrt [ (7 -1)^2 + (3 -1)^2 ]  = sqrt [ 6^2 + 2^2 ]  = sqrt [40]

AD  = sqrt [ (-5 -1)^2 + (8 -1)]  = sqrt [ (-6)^2 + 7^2]  = sqrt [36 + 49] = sqrt [85]

This disqualifies the square....!!!

BC  = sqrt [ (1 -7)^2 + (12 -3)^2 ]  = sqrt [ 6^2 + 9^2]  = sqrt [ 36 + 81] = sqrt [117]

This disqualifies the rectangle, as we, because BC > AD

The only thing left is that it could be an trapezoid.......this will be true if  slope of BC  = slope of AD  or if  the slope of DC  = slope of AB

Slope of BC = [12 -3] / [1 - 7]  = 9/ -6  = -3/2

Slope of AD  = [8 -1] / [-5 -1]  = 7/-6  = -7/6

Slope of DC  = [8-12] / [ -5 -1]  = -4/-6  = 2/3

Slope of AB  = [3-1] / [ 7-1] = 2/6  = 1/3

So...it's just a quadrilateral

Here's a pic  ......