I think it's obvious that the given point had to be (p,q) in the fourth
quadrant.
All first quadrant points are
All second quadrant points are
All third quadrant points are
All fourth quadrant points are
So if (p,q) is a point in the fourth quadrant, then p is
POSITIVE and q is NEGATIVE, so -p is NEGATIVE. So (q,-p) is
(NEGATIVE,NEGATIVE) so it's in the third quadrant.
Edwin