In quadrilateral pqrs, the coordinates are p(o, o), q(a+c, o), r(2a+c, b., and s(a, b. how can you use coordinate geometry to show that the diagonals are perpendicular?

Given:
  Quadrilateral PQRS
  P(o, o), Q(a+c, o), R(2a+c, b), S(a, b)
Find:
  whether the diagonals are perpendicular using coordinate geometry
Solution:
  If the diagonals are perpendicular, their slopes multiply to give -1.
The slope of PR is
  (b-o)/(2a+c-o)
The slope of QS is
  (b-o)/(a-(a+c)) = (b-o)/(-c)
The product of these slopes is
  (b-o)·(b-o)/((2a+c-o)(-c))
This value will not be -1 except for very specific values of a, b, c, and o.

It cannot be concluded that the diagonals of PQRS are perpendicular based on the given coordinates.

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