Find an equation for the perpendicular bisector of the line segment whose endpoints are (-1,5) and (-7, -7).

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

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = , where

∵ A line passes through points (-1, 5) and (-7, -7)

∴ x1 = -1 ad y1 = 5

∴ x2 = -7 and y2 = -7

→ Use the rule of the slope above to find the slope of the line

∵ m = = = = 2

∴ m = 2

→ Reciprocal the value of m and change its sign to find the slope of

  the line perpendicular line

∴ m⊥ =

→ Substitute in the form of the equation above

∵ y = x + b

∵ The ⊥ line is also the bisector of the given line, find the mid-point

   of the given line because it is also lying on the ⊥ line

∵ M = () =  () = (-4, -1)

∴ M = (-4, -1)

→ Substitute the coordinates of M in the equation of the ⊥ line above

∵ x = -4 and y = -1

∴ -1 = (-4) + b

∴ -1 = 2 + b

→ Subtract 2 from both sides

∴ -3 = b

→ Substitute the value of b in the equation

∴  y =   x + -3

∴ y =   x - 3

∴ The equation of the perpendicular bisector is y =   x - 3

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step-by-step explanation: