Question 212212
Two points are given from each of two lines: L1 and L2.  Without graphing the points, determine if the lines are parallel, perpendicular, or neither. L1:(3,-2) and (4,8)  L2: (1,6) and (7,-18)


Step 1.  Need to determine the slopes of L1 and L2.  Let m1 be the slope of L1 and m2 be the slope of L2.  


Note 1:  The lines are perpendicular if the product of the slopes is equal to -1.


Note 2:  The lines are parallel if the slopes are equal.


Note 3:  And neither if it does not satisfy Notes 1 and 2 above.


Step 2.  Slope of Line 1( L1)is given as


{{{m = (y2-y1)/(x2-x1)}}}


Given L1:(3,-2) and (4,8), then let y2=8, x2=4, x1=3, y1=-2


{{{m1 = (8-(-2))/(4-3)}}}


{{{ m1 = 10/1}}}


{{{ m1 = 10}}}


Step 3.  Slope of Line 2( L2)is given as


L2: (1,6) and (7,-18), then let x1=1, y1=6, x2=7, and y2=-18



{{{m2 = (-18-6)/(7-1)}}}


{{{ m2 = -24/6}}}


{{{ m2 = -4}}}


Step 4.  The product of m1 and m2 is not equal to -1, so they are not perpendicular. 


The slopes are not equal, so they are not parallel.


ANSWER:  So the lines are neither perpendicular nor parallel.


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