Question

Can someone help me? Porfavor? (:

the vertices of square PQRS are P(-4,0) Q(4,3) R(7,-5) S(-1,-8). show that the diagonals of square PQRS are congruent perpendicular bisectors of each other.

Answer 1

Mid point of P and R is ((-4+7)/2 ,(0-5)/2) = (3/2,-5/2)
Mid point of Q and S is ((4-1)/2 ,(3-8)/2) = (3/2,-5/2)

So mid point of both is same so they bisect each other.
For perpendicular,
RP(vector) = (-4-7,0+5) = (-11,5)
QS(vector) = (-1-4,-8-3) = (-5,-11)
RP.QS = 55-55=0
So Digonals are perpendicular

Length of PR =sqrt(11^2 + 5^2) = Length of QS

Hence Proved Congruent Perpendicular Bisectors.

Answer 2

my teacher wants me to prove i t and i've tried to work it..but it just won't come out..