Find an equation for the perpendicular bisector of the line segment whose endpoints are (-5,6) and (9,2)

  7x -2y = 6

Step-by-step explanation:

The perpendicular bisector has a slope that is the opposite of the reciprocal of the slope of the segment between the two points. It must go through the midpoint of the segment.

The latter can be found by averaging the coordinates of the end points:

  ((-5, 6) +(9, 2))/2 = ((-5+9)/2, (6+2)/2) = (2, 4)

The difference in endpoint coordinates is ...

  (Δx, Δy) = (9-(-5), 2-6) = (14, -4)

For our purpose, we're only interested in the ratio of these values, so we can divide both by the common factor of 2:

  (Δx, Δy) = (7, -2)

A line perpendicular to this segment through the point (h, k) can be written as ...

  Δx·x +Δy·y = Δx·h +Δy·k

  7x -2y = 7(2) -2(4)

  7x -2y = 6 . . . . . . . standard form equation for the perpendicular bisector

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