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The equation of the perpendicular bisector of the line segment joining the points \((-3,8)\) and \((-5,4)\) is \(y = mx + b\). Find \(m+b \).

Note: The perpendicular bisector of the line segment \(\overline{AB}\) is the line that passes through the midpoint of \(\overline{AB}\) and is perpendicular to \(\overline{AB}\).

 Apr 4, 2020
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The slope of the line segment is (8 - 4)/(-5 - (-3)) = -2, so the slope of the perpendicular bisector is 1/2.  The midpoint is (-4,6), so by point-slope form, the equation fo the line is y - 6 = 1/2(x + 4).  Then y = 1/2*x + 8, so m + b = 1/2 + 8 = 17/2.

 Apr 4, 2020

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