Question

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 and the slope of SR and PQ is . The length of SQ and RP are both . The midpoint of both diagonals is , the slope of RP is 7, and the slope of SQ is .

Answer 1

Answer: the correct answer is letter D, I just took the test and got it right on edg

Answer 2

Answer:

Step-by-step explanation:

Given is a square PQRS.  Its diagonals are PR and QS.

To prove that PR is perpendicular to QS

We have been given as

SP = PQ =RQ =SR =5.

Using Pythagorean theorem we have

both diagonals will equal

$5\sqrt2$

If P is the origin, (say) then coordinates of vertices would be (0,0) (5,0) (5,5) and (0,5)

Mid point would be (2.5,2.5) for both

Slope of RP = change in y coordinate/change in x coordinate

= 1

Slope of QS = 5/-5 = -1

Product of the two slopes = -1

Hence the two diagonals are perpendicular