The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
The points (−3, 4), (2, −1), (5, 2), and (0, 7) are vertices of a quadrilateral. Show that the quadrilateral is a rectangle.(Hint: Show that the quadrilateral’s opposite sides are the same length and that the two diagonals are the same length.)
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