Find the equation of the perpendicular bisector of the given segment by following these steps. 1. determine the slope of the given segment.

The equation of the perpendicular bisector is  2x + 3y - 3 = 0

Step-by-step explanation:

* How to find the equation of a line from two points (x1 , y1)

 and (x2 , y2) lie on it

- Find the slope of the line using the rule

 The slope (m) = (y2 - y1)/(x2 - x1)

- Use the rule of the equation y - y1 = m (x - x1), where m is

 the slope of the line and (x1 , y1) is a point on the line

* Remember if two line are perpendicular, then the product of

 their slopes = -1, that means one of them is an additive inverse

 and multiplicative inverse to the other

 # Ex: if the slope of a line is a/b, then the slope of the

   perpendicular to it is -b/a

* Now lets read the problem, we need the equation of the

 perpendicular bisector to the line that passes through the

 points (2 , 4) and (-2 , -2)

- Find the slope of the line in the graph by using the given points

 # m = (-2 - 4)/(-2 - 2) = -6/-4 = 3/2

∴ The slope of the perpendicular line = -2/3 ⇒ multiplicative

   inverse and additive inverse of it

* Bisector means intersect it in the mid-point of the given line

- The rule of the mid-point is [(x1 + x2)/2 , (y1 + y2)/2]

∴ The mid-point of the line is [(2 + -2)/2 , (4 + -2)/2] = (0 , 1)

* Now we have the slope and a point on the line, to find the

 equation of the perpendicular bisector its slope is -2/3 and

 a point (0 , 1)

∴ The equation: y - 1 = -2/3 (x - 0)

  The equation : y - 1 = -2/3 x ⇒ Multiply both sides by 3

  The equation : 3y - 3 = -2x ⇒ collect x , y in the same side

  The equation : 2x + 3y - 3 = 0

* The equation of the perpendicular bisector is  2x + 3y - 3 = 0