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.
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
