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The equation of the perpendicular bisector of the line segment joining the points (-3,8) and (-5,4) is y = mx + b. Find m+b. Note: The perpendicular bisector of the line segment \overline{AB} is the line that passes through the midpoint of \overline{AB} and is perpendicular to \overline{AB}.

 Mar 1, 2020
 #1
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The slope of the line segment whose endpoints are (-3,8) and (-5,4) is found by using the equation: 

        m  =  (y2 - y1) / (x2 - x1)

--->  m  =  (4 - 8) / (-5 - -3)  =  -4 / -2  =  2

Therefore, the slope of the perpendicular is  =  -1/2

 

The midpoint of a line segment is found by the equation:  midpt  =  ( (x1 + x2) / 2, (y1 + y2) / 2 ) 

      =  ( (-3 + -5) / 2, (8 + 4) / 2 )  =  ( -8/2, 12/2 )  =  ( -4, 6 )

 

If you know both the slope of a line and a point of the line, you can find the equation by using:  y - y1  =  m(x - x1)

      y - 6  =  (-1/2)(x - -4)     --->     y - 6  (-1/2)(x + 4)     --->     y - 6  =  (-1/2)x - 2     --->     y  =  (-1/2)x + 4

 

Now, find m, b, and m + b.

 Mar 1, 2020
 #2
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How do you find B?

 Mar 1, 2020

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