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Find the distance between the graphs of 5x-12y+45=0 and 5x-12y+46=0.

 Nov 23, 2020
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Rewrite  the equations as

 

y= (5/12)x + 45/12       →         y = (5/12)x + 15/4    (1)

 

y = (5/12)x + 46/12      →         y  = (5/12)x  + 23/6

 

A perpendicular  line  to  both of  these  will have a slope of  (-12/5)

And if we let this line pass through  (0, 23/6)    we  have  the following equation

 

y =  (-12/5)x + 23/6

 

To find the  x intersection of  this line and  (1)  we have

 

(5/12)x + 15/4 =  (-12/5)x + 23/6

 

(5/12 + 12/5)x  =  23/6 - 15/4

 

(169/60)x = 1/12      

 

x = (1/12) (60/169)  = 5/169

 

And y = (5/12) (5/169)  + 15/4   =  3815/1014

 

The distance between these lines  =

 

sqrt  [ (5/169)^2  +  ( 23/6 - 3815/1014)^2 ]   =  1/13  units

 

 

cool cool cool

 Nov 24, 2020

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