Final answer:
To create a trapezoid RSTU that is not congruent to trapezoid PQMN, ensure the side lengths or angles are different, while maintaining one pair of parallel sides.
Step-by-step explanation:
To determine coordinates for trapezoid RSTU that are not congruent to trapezoid PQMN, you must ensure that RSTU has different side lengths or angles than PQMN.
However, to still form a trapezoid, two sides of RSTU must be parallel, while the other two are not. An example of this would be if trapezoid PQMN has coordinates P(1,1), Q(3,1), M(2,3), and N(4,3), then trapezoid RSTU could have coordinates R(0,0), S(5,0), T(3,2), and U(2,2).
In this case, while PQMN has a pair of parallel sides PM and QN both having a length of 2 units, RSTU has a pair of parallel sides RS and TU where RS is 5 units long, which ensures that RSTU is not congruent to PQMN. Congruent figures have the same size and shape; thus, changing the length of one or more sides ensures non-congruence.