Question

Find the equation of the perpendicular bisector of the line segment with endpoints (-6,-6) and (3,6)

Answer 1

find the midpoint of the line segment

x = (-6 + 3)/2 y = (-6 + 6)/2

the midpoint is (-1.5, 0) the bisector passes through the midpoint.

next find the gradient of the line

m = rise/run

m = ( 6 - -6)/(3 - - 6)

m = 12/9

m = 4/3

so the slope is of the line segment is 4/3

then the perpendicular line segment is - 3/4

the equation of the line is

y = -3/4x + b

substitute the values from the midpoint to evaluate b and get the equation of the line.