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Product of slopes of pirpendicular lines is -1. Slope of x-axis is 0, slope of y-axis is “infinity”. But, 0*infinity is not -1 why?

Product of slopes of pirpendicular lines is -1. Slope of x-axis is 0, slope of y-axis is “infinity”. But, 0*infinity is not -1 why?

Grade:11

3 Answers

Nicho priyatham
625 Points
8 years ago
we say product of slopes  -1 if perpendicular when both slopes are finite
tan (teta)=(m2-m1)/1+m1m2 
so if perpendicular denominator zero m1m2 =-1
if one of them is infinite then use the formula again 
tan (teta)=(m2-m1)/1+m1m2
              =(1-(m1/m2 ) )/(m1+1/m2 )
now put m2 infinit  and m1 =o
u get tan (teta )as 1/0 so teta=900    
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Raghu Vamshi Hemadri
72 Points
8 years ago
If product of slopes of 2 lines is -1 then they are perpendicular. But, the converse may not be true always. The statement of converse clearly has a limitation in it i.e., if the lines are parllel to the coordinate axes this statement dosent hold good.
 
Raghu Vamshi Hemadri
72 Points
8 years ago
If product of slopes of 2 lines is -1 then they are perpendicular. But, the converse may not be true always. The statement of converse clearly has a limitation in it i.e., if the lines are parllel to the coordinate axes this statement dosent hold good.

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