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N76 [4]
3 years ago
6

Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other? The length of SP, PQ, RQ, an

d 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 .
Mathematics
2 answers:
MatroZZZ [7]3 years ago
8 0

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

pochemuha3 years ago
6 0

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

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