Final answer:
To determine the type of quadrilateral from given coordinates, calculate the lengths of sides and diagonals using the distance formula. These lengths reveal whether it's a square (all sides and diagonals equal), rectangle (opposite sides and diagonals equal), or a parallelogram (opposite sides equal and diagonals bisect, but don't need to be equal).
Step-by-step explanation:
I believe there may be a typographical error in your question as madrilateral is not a recognized term in geometry. Assuming you mean to verify if the quadrilateral formed by the points R(-4,1),S(-2,5),T(2,1), and U(2,-7) is a specific type (rectangle, parallelogram, square, etc.), you'll need to calculate the lengths of the sides and diagonals using the distance formula.
If all four sides are the same length, and the diagonals are the same length, it is a square. If only opposite sides are the same length, it could be a rectangle or parallelogram. If the diagonals are equal and intersect at a right angle, it is a rectangle. For a parallelogram, the opposite sides are equal, and the diagonals bisect each other but are not necessarily of equal length. Also, no sides are perpendicular in a parallelogram.
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