The vertices of square pqrs are p(−4, 7), q(5, 4), r(2,−5) and s(−7,−2). which of the following shows that its diagonals are congruent perpendicular bisectors of each other?

Option (A)

Step-by-step explanation:

The vertices of square PQRS are P(−4, 7), Q(5, 4), R(2,−5) and S(−7,−2).

Now, Join the diagonals PR and QS,

now, PR=

=

=

Also, QS=

=

=

Therefore, PR is congruent to  QS that is PR≅QS.

Slope of PR=

=

Slope of QS=

Thus, PR⊥QS.

Now, Mid point of PR=

=

=

Also, mid point of QS=

=

Therefore, (-1,1) is the mid point of both PR and QS, so PR and QS bisect each other.

Hence, option (A) is correct.

 The first option is correct.

Step-by-step explanation:  Given that the vertices of square PQRS are P(−4, 7), Q(5, 4), R(2,−5) and S(−7,−2). So, PR and QS are its two diagonals.

First, we will measure PR and QS as follows.

Therefore, PR = QS = 3√20.

Now, slope of PR is

and slope of QS is

Hence, PR ⊥ QS.

Again, mid-point of PR is

and mid-point of QS is

Thus, the correct option is

43

step-by-step explanation: