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A statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is: option D.
<h3>How to calculate the slope of a line?</h3>Mathematically, the slope of a line is given by the following formula;
For line RP, we have:
Slope RP = 7.
For line SQ, we have:
Slope SQ = negative one-sevenths.
For the midpoint, we have:
In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint on x-coordinate = (8 + 1)/2 = 9/2 = 4.5.
Midpoint on y-coordinate = (9 + 2)/2 = 11/2 = 5.5.
In conclusion, a statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is that the midpoint of both diagonals is (4.5, 5.5), the slope of RP is 7, and the slope of SQ is negative one-sevenths.
Read more on squares here: brainly.com/question/2882032
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