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The graph of the line x + y = b is a perpendicular bisector of the line segment from (1,3) to (7,9). What is the value of b?

 
 Nov 21, 2020
 #1
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The slope of this segment  is  [ 9 - 3 ] / [ 7 - 1 ]  =  6/6  = 1

The perpendicular line to this segment will have a  negative reciprocal slope   =  -1

 

Since this line is a perpendicular bisector, we need to find the  mdpoint of the segment.....this is given by

 

(  [ 1+ 7] / 2 , [ 3 + 9] / 2  )    =   (8/2 , 12/2 )  =  (4, 6)

 

The equation of the perpendicular line is

 

y = -1 ( x -4)  + 6

 

y = -x + 4 + 6      add x to both sides  and simplify

 

x + y  = 10

 

So...b  =  10

 

cool cool cool

 
 Nov 22, 2020

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