Question 163652
You need to calculate the slope for both lines and compare.
Parallel lines have identical slopes {{{m[1]=m[2]}}}
Perpendicular lines have slopes that are negative reciprocals {{{m[1]*m[2]=-1}}}.
If it meets neither of these, then it fits the neither category.
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First calculate the slopes,
{{{m=(y[2]-y[1])/(x[2]-x[1])}}}
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{{{m[1]=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m[1]=(4-0)/(7-1)}}}
{{{m[1]=(4)/(6)=2/3}}}
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{{{m[2]=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m[2]=(6-0)/(3-7)}}}
{{{m[2]=(6)/(-4)=-3/2}}}
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Looks like they're perpendicular because,
{{{m[2]=-1/m[1]}}}
of
{{{m[1]*m[2]=-1}}}
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You can graph the points connect them with lines and check to verify your answer.
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{{{drawing( 300, 300, -2, 10, -2, 10,grid( 1 ),
circle( 1, 0, .2 ),
circle( 7, 4, .2 ),
circle( 7, 0, .2 ),
circle( 3, 6, .2 ),
green(line(7,0,3,6)),
green(line( 1,0,7,4)))}}}