Question

ures in the coordinate plane. which statement proves that the diagonals of square pqrs are perpendicular bisectors of each other? the midpoint of both diagonals is (4 1/2, 5 1/2), the slope of rp is 7, and the slope of sq is -1/7. the slope of rp and rq is -1/7 and the slope of sr and pq is 7.

Explanation:

Step1: Recall properties of perpendicular bisectors

For two lines to be perpendicular bisectors of each other, they must have the same mid - point (bisect each other) and their slopes must be negative reciprocals (perpendicular).

Step2: Analyze the first statement

If the mid - point of both diagonals is the same, it means they bisect each other. And if the slope of one diagonal is \(m_1\) and the slope of the other is \(m_2=-\frac{1}{m_1}\), they are perpendicular.

Answer:

The first statement "The midpoint of both diagonals is \((4\frac{1}{2},5\frac{1}{2})\), the slope of \(RP\) is 7, and the slope of \(SQ\) is \(-\frac{1}{7}\)" proves that the diagonals of square \(PQRS\) are perpendicular bisectors of each other.