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# equation of a perpendicular bisector

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Find an equation for the perpendicular bisector of the line segment whose endpoints are (9,-3) and (-5,-7).

Feb 28, 2021

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(9, -3) and (-5, -7)

midpoint: $$(\frac{9-5}{2}, \frac{-3-7}{2}) = (2, -5)$$

slope: $$\frac{-7+3}{-5-9} = \frac{2}{7}$$

perpendicular bisector has a perpendicular slope and passes through the midpoint:

$$y+5 = \frac{2}{7}(x-2)$$

Feb 28, 2021