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Let line t be the line represented by 3x+4y = 5 and let line p  be the line perpendicular to line t and containing the point (5,5) . What is the x-coordinate of the point common to line t and line p ? Express your answer as a common fraction.

tertre  Apr 18, 2017
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3x + 4y  = 5     the slope of this line  =   -3/4.....so....the slope of a perpendicular line will be 4/3

 

And the equation of a line with this slope passing through (5,5)   is

 

y = (4/3) (x - 5) + 5

 

y = (4/3)x - 20/3 + 5

 

y  = (4/3)x - 5/3

 

Subbing this into  3x + 4y  = 5 for y , we have

 

3x + 4[ (4/3)x - 5/3]  = 5

 

 

3x + (16/3 )x - 20/3  = 5     simplify

 

(25/3)x =  35/3

 

25x  =  35       divide both sides by  25

 

x  = 35/25   =  7/5      and this is the x coordinate of the intersection of line t and p

 

 

 

cool cool cool

CPhill  Apr 18, 2017

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