How do i determine an equation for the perpendicular bisector of the line segment joining A(3,6) and B(-1,2)?

Answer 1

The perpendicular bisector goes through the midpoint of the segment. To find the x-value of the midpoint just add the 2 x-values and divide by 2 so (3 + -1)/2 = 1. To find the y-value of the midpoint just add the 2 y-values and divide by 2 so (6 + 2)/2 = 4. So the midpoint is (1, 4).

The perpendicular to a segment will have a slope that is the negative reciprocal of the slope of that segment. To find the slope of the segment, use the slope equation: m = (y₂ - y₁)/(x₂ - x₁) = (2 - 6)/(-1 - 3) = -4/-4 = 1. That means the slope of the perpendicular is -1.

So, using the point-slope form of a line, the equation of the perpendicular bisector is (y - 4) = -1(x - 1)

If you want this in the slope-intercept form, just multiply it out and combine like-terms:

(y - 4) = -1(x - 1)

y - 4) = -x + 1

y = -x + 5