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Answer:
x +3y = -3
Explanation:
The midpoint of the segment with the given end points is ...
M = ((4, 1) +(2, -5))/2 = (6, -4)/2 = (3, -2)
The difference between coordinates of the given points is ...
(∆x, ∆y) = (4, 1) -(2, -5) = (2, 6)
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The equation of the perpendicular bisector can be written as ...
∆x(x -h) +∆y(y -k) = 0 . . . . line through (h, k) ⊥ to one with slope ∆y/∆x
2(x -3) +6(y -(-2)) = 0
2x +6y +6 = 0 . . . . . simplify to a general-form equation
To put this in standard form, we need the constant on the right, and all numbers mutually prime. We can subtract 6 and divide by 2 to get there.
2x +6y = -6
x + 3y = -3