SOLUTION: Use the distance formula to find an equation of the perpendicular bisector of the line segment between the points (4,3) and (-2,5)

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Question 1160443: Use the distance formula to find an equation of the perpendicular bisector of the line segment between the points (4,3) and (-2,5)
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Use the distance formula to find an equation of the perpendicular bisector of the line segment between the points (4,3) and (-2,5)
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Find the midpoint
It's the average of x & y separately
x: (4-2)/2 = 1
y: (3+5)/2 = 4
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The MP is (1,4)
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Find the slope of the line thru the 2 points:
slope = diffy/diffx = (5-3)/(-2-4) = -1/3
The slope, m, of lines perpendicular is the negative inverse. m = 3
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Use y - y1 = m*(x - x1) where (x1,y1) is the Midpoint.
y-4 = 3*(x-1)
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I don't see how the distance formula is involved.


Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

Let (x,y) be the current point on the perpendicular bisector.


Its distance from the point (4,3) is  .


Its distance from the point (-2,5) is  .


The distances are equal

     = .


Square both sides

    (x-4)^2 + (y-3)^2 = (x+2)^2 + (y-5)^2.


Simplify

    x^2 - 8x + 16 + y^2 - 6y + 9 = x^2 + 4x + 4 + y^2 - 10y + 25

    -8x - 4x + (-6y + 10y) = 4 + 25 - 16 - 9

    -12x + 4y = 4

     3x - y = -1.     ANSWER

Solved.


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