Please find attached the drawing of the polygon with vertices, (-5, 6), (4, 1), (4, -7), and (-5, -2), which is a parallelogram, created with MS Excel
The steps used to find the shape of the polygon are as follows;
A polygon with vertices (-5, 6), (4, 1), (4, -7), (-5, -2), has the shape of a parallelogram
The shape is a parallelogram because, the segment with vertices, (-5, 6), (-5, -2) and (4, 1), (4, -7) are vertical segments and are therefore, parallel
The vertical lengths of the segments (-5, 6), (-5, -2) and (4, 1), (4, -7) are the same, which indicates that the transversals, (-5, 6), (4, 1), and (4, -7), (-5, -2) are parallel
The vertical and horizontal lengths of the segment with vertices (-5, 6), (4, 1), and (4, -7), (-5, -2), are the same, therefore, the segments have the same lengths
Therefore, the figure with two pairs of facing parallel and congruent sides is a parallelogram
The diagram of the polygon, created with MS Excel using the coordinates in the question is attached