Find the equation of the perpendicular bisector of points (2, -5) and (8,-3)

Question

Find the equation of the perpendicular bisector of points (2, -5) and (8,-3). I need help with my exam that is tomorrow

Answer 1

First, let's find the midpoint of the segment connecting the points (2,-5) and (8,3).

x_m = x₁ + x₂        and    y_m = y₁ + y₂

              2                                 2

x_m = 2 + 8         and     y_m = -5 - 3

             2                                    2

x_m = 5       and     y_m = -4

M(5, -4)

 

Now, let's find the slope of the line containing those two given points.

m = y₂ - y₁ = -3 + 5  = 2 = 1

       x₂ - x₁       8 - 2       6     3

Since perpendicular lines have slopes that are negative reciprocals of each other, the new line will have a slope of -3.

 

Use the Point-Slope form of the equation of a line:

y - y₁ = m(x - x₁)

y + 4 = -3(x - 5)

y  + 4 = -3x + 15

y = -3x + 11