Question 431948
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Hi
Using the point-slope formula, {{{m =(y[2] - y[1])/(x[2] - x[1])}}}
P1(4,-5)
P2(6,-9)  m = 4/-2 = -2
Q1(5,-4)
Q2(1, 4)  m = -8/4 = -2
line through P1 and P2 is parallel to the line through Q1 and Q2.

P1(5, 1)
P2(3,-2) m = 3/2
Q1(0,-2)
Q2(3,-4) m = 2/-3 = -2/3
line through P1 and P2 is perpendicular to the line through Q1 and Q2.

P1(1,-1)
P2(3,-2) m = 1/-2 = -1/2
Q1(-4,1)
Q2(2,-5) m = 6/-6 = -1
the line through P1 and P2 is neither parallel nor perpendicular 
to the line through Q1 and Q2.