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A line passes through the midpoint of $(1,2)$ and $(19,4)$. The line is perpendicular to a line through $(0,7)$ and $(4,-3)$. What is the $y$-coordinate of the line when $x=20$?

 May 4, 2018
 #1
avatar+101322 
+1

Midpoint  of  (1,2) , (19,4)   =  ( 10, 3)

 

The line containing points  (0,7) and (4, - 3)  has a slope of    [ -3 - 7] / [4 - 0]  =  -10/4  = -5/2

 

So....a line perpendicular to this will have a slope of   2/5

 

So....the equation of this line is

 

y  = (2/5)(x - 10) + 3

 

y = (2/5)x - 4 + 3

 

y = (2/5)x - 1

 

So....when x  = 20

 

y =  (2/5)(20) - 1

 

y  = 8 - 1

 

y  = 7

 

EDITED TO CORRECT A SIGN ERROR

 

 

cool cool cool

 May 4, 2018
edited by CPhill  May 4, 2018
edited by CPhill  May 4, 2018
 #2
avatar+603 
+1

It was actually 7, thank you though

gueesstt  May 4, 2018

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