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Write the equation of the perpendicular bisector of AB

 

#1       A) (3, -6) B) (7, 2) 

 

 

#2       A) (2, 5)   B) (6, -7) 

 

#3       A) (8, 1)  B) (0, -1) 

 

#4       A) (7, 9)   B) (1, 5) 

 Feb 27, 2019
 #1
avatar+844 
0

1. find gradient 2--6/7-3 = 8/4 = 2

m*m = -1

m= -0.5

sub the information u know into formula

y = mx + c  or   y - y1 = m(x -x1)

y = -0.5x + 0.5

 Feb 27, 2019
edited by YEEEEEET  Feb 27, 2019
edited by YEEEEEET  Feb 27, 2019
 #2
avatar+19832 
+2

Here is how I would do the second one:

find slope  =  rise/run  = y1-y2 / x1-x2  =  (5- -7)/(2-6) = 12/-4 = -3

Perpindicular slope is    -  1/(-3) = 1/3

 

Find the midpoint of AB

  x      (2+6)/2 = 4

  y      (5+ -7)/2 = -1      so midpoint is    (4,-1)   and slope is 1/3

            line is     y = 1/3  x  + b     sub in your midpoint to calculate  'b'

                          -1 = 1/3 (4) + b    results in b = -7/3

 

y = 1/3 x -  7/3

 

Here is a picture:

 Feb 27, 2019
edited by ElectricPavlov  Feb 27, 2019
edited by ElectricPavlov  Feb 27, 2019
 #3
avatar+104899 
+1

#3     A) (8, 1)  B) (0, -1) 

 

1)  Find the midpoint  =  ( [ 8 + 0] / 2, [ -1 + 1] / 2)  =  (4, 0 )

2) Find the slope  =  [ -1 -1 ] / [ 0 - 8 ] =   -2/ -8 =  1/4

3) Take the negative reciprocal o the slope =  -4

 

Using the midpoint and  (3)   we have

 

y = -4(x - 4)

 

y = -4x + 16

 

 

cool cool cool

 Feb 27, 2019
 #4
avatar+104899 
+1

#4       A) (7, 9)   B) (1, 5) 

 

Midpoint  ( [ 7 + 1] /2 , [ 5 + 9] /2)    =  ( 4, 7)

Slope  =  [9 - 5 ] / [ 7 - 1 ] =  4/6 = 2/3

Neg reciprocal slope = -3/2      (1)

 

Using  midpoint  and  (1)   we have

 

y = (-3/2) ( x - 4) + 7

 

y = (-3/2)x + 6 + 7

 

y = -(3/2)x + 13

 

 

cool cool cool

 Feb 27, 2019

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