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Consider the line segment whose endpoints are the x- and y-intercepts of  4 x + y -24 = 0 , and let line  l be the perpendicular bisector of this segment.  If line l  passes through  (11, a) , what is the value of  a  ?

 Jan 15, 2021
 #1
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4x + y  - 24   =  0

 

x intercept  =  6           y intercept  =  24

 

So   the points  are   ( 6,0)  and ( 0,24)

 

The midpoint of this segment =    ( 3, 12)

 

And the  slope of this segment =  -24/6 =  -4

 

So.....the equation of the  perpendicular  bisector is

 

y= (1/4) (x - 3) + 12

 

4y  = x - 3 +  48

 

4y  =  x  + 45

 

x - 4y + 45  =  0

 

When x = 11  then  

 

11  - 4a  + 45  =  0

 

56- 4a  =  0

 

56  = 4a

 

a  = 56/4  =  14

 

See the graph here :  https://www.desmos.com/calculator/bi4jwkbp07

 

 

cool cool cool

 Jan 15, 2021

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