Math CentralQuandaries & Queries


Question from Emily, a student:

How do you solve perpendicular bisectors with a slope and a point?


I assume the type of question you have is

Find the equation of the line which passes through the point (3, -5) and is perpendicular to a line with slope 2/3.

The key here is that if a line has slope m (m ≠ 0) then a line perpendicular to it has slope -1/m. Thus the line you are looking for in the example above will have slope -3/2. Thus you need the line with slope -3/2 which passes through (3, -5). The point-slope equation of the line is then

(y + 5) = -3/2 (x - 3)


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