Hi

Using the point-slope formula, 

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. 

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