Geometry- Mid point magic

Question

Draw a pair of X-Y axes on graph paper and plot four points, one in each quadrant such that you create a quadrilateral that is not special

Answer 1

So, there are many potential solutions to this problem, but a simple way to solve this is to AVOID plotting points that result in...

1. Two lines being parallel (i.e. same slope)
2. Two lines being congruent (i.e. distance/length is the same)

If you avoid these three things, you will prevent creating all Parallelograms (which includes but is not limited to rectangles, rhombi, and squares), Trapezoids, and Kites.

This is because by definition, all of these quadrilaterals have at least one of these properties. Parallelograms have opposite sides that are parallel and congruent, Trapezoids have parallel bases, and Kites have two pairs of congruent adjacent sides.

This includes all special quadrilaterals, so whatever is left must be not special. Your job will be to make such a shape and then verify that it is not special through the slope and distance formulas. Hope this helps!