On a coordinate plane, square P Q R S is shown. Point P is at (4, 2), point Q is at (8, 5), point R is at (5, 9), and point S is at (1, 6). Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other?

The length of SP, PQ, RQ, and SR are each 5.
The slope of SP and RQ is Negative four-thirds and the slope of SR and PQ is Three-fourths.
The length of SQ and RP are both StartRoot 50 EndRoot.
The midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of RP is 7, and the slope of SQ is Negative one-sevenths.