SOLUTION: The question is write an equation for the perpendicular bisector of the line segment joining the two points? the points are (0,0)(-8,-10) how would you solve this

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Question 38557This question is from textbook
: The question is write an equation for the perpendicular bisector of the line segment joining the two points?
the points are (0,0)(-8,-10)
how would you solve this This question is from textbook

Found 2 solutions by venugopalramana, AnlytcPhil:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
the question is write an equation for the perpendicular bisector of the line segment joining the two points?
the pionts are A-(0,0).............AND B-(-8,-10)
how would you solve this
MID POINT OF AB ...SAY....C...IS (0-8)/2,(0-10)/2=(-4,-5)
SLOPE OF AB =(0+10)/(0+8)=10/8=5/4
SLOPE OF PERPENDICULAR TO AB IS -1/(5/4)=-4/5
PERPENDICULAR BISECTOR IS PERPENDICULAR TO AB AND PASSES THROUGH ITS MID POINT C.HENCE ITS EQN. IS
Y+5=(-4/5)(X+4)
5Y+25=-4X-16
4X+5Y+41=0

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
The question is write an equation for the perpendicular
bisector of the line segment joining the two points?

the points are (0,0)(-8,-10)

1. First we find the midpoint between (0,0) and (-8,-10)
because the perpendicular bisector must pass through 
its midpoint.

2. Second we find the slope of the line through 
   (0,0) and (-8,-10)

3. Third we find the slope of the perpendicular bisector 
   by
   A. taking the reciprocal of the slope of the line 
      thru (0,0) and (-5,10)
   B. Multiplying this result by -1, which means 
      "changing the sign"

4. Fourth, we find the equation of the perpendicular 
   bisector using the point-slope form.

5. Simplify 

Here goes:

1. First we find the midpoint between (0,0) and (-8,-10)
because the perpendicular bisector must pass through 
its midpoint.

Midpoint = ( (x1+x2)/2, (y1+y2)/2 )

Midpoint = ( [0+(-8)]/2, [0+(-10)]/2 )

Midpoint = ( -8/2, -10/2 )

Midpoint = (-4,-5)  

2. Second we find the slope of the line through
   (0,0) and (-8,-10)

    y2 - y1
m = ———————
    x2 - x1

    (-10) - (0)
m = ————————————
     (-8) - (0)

m = (-10)/(-8)

m = 5/4

3. Third we find the slope of the perpendicular bisector 
   by
   A. taking the reciprocal of the slope of the line 
      thru (0,0) and (-5,10)
      
      reciprocal of 5/4 is 4/5

   B. Multiplying this result by -1, which means 
      "changing the sign"

      changing the sign of 4/5 we have -4/5

4. Fourth, we find the equation of the perpendicular 
   bisector using the point-slope form.

        y - y1 = m(x - x1) where 

    m = -4/5 and (x1,y1) = Midpoint = (-4,-5)

      y - (-5) = -4/5[x - (-4) ]

5. Simplify

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

         y + 5 = -4/5x - 16/5

             y = -4/5x - 16/5 - 5

             y = -4/5x - 16/5 - 25/5

             y = -4/5x - 41/5

If you like you can put the equation in standard
form by clearing of fractions, getting x term first,
y term second, equal sign third and number fourth:

            5y = -4x - 41

       4x + 5y = -41

Edwin
AnlytcPhil@aol.com