Answer:
The equation of the perpendicular bisector is y = [tex]\frac{-1}{2}[/tex] 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 = [tex]\frac{y2-y1}{x2-x1}[/tex] , 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 = [tex]\frac{-7-5}{-7--1}[/tex] = [tex]\frac{-12}{-7+1}[/tex] = [tex]\frac{-12}{-6}[/tex] = 2
∴ m = 2
→ Reciprocal the value of m and change its sign to find the slope of
the line perpendicular line
∴ m⊥ = [tex]\frac{-1}{2}[/tex]
→ Substitute in the form of the equation above
∵ y = [tex]\frac{-1}{2}[/tex] 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 = ([tex]\frac{-1+-7}{2},\frac{5+-7}{2}[/tex]) = ([tex]\frac{-8}{2},\frac{-2}{2}[/tex]) = (-4, -1)
∴ M = (-4, -1)
→ Substitute the coordinates of M in the equation of the ⊥ line above
∵ x = -4 and y = -1
∴ -1 = [tex]\frac{-1}{2}[/tex] (-4) + b
∴ -1 = 2 + b
→ Subtract 2 from both sides
∴ -3 = b
→ Substitute the value of b in the equation
∴ y = [tex]\frac{-1}{2}[/tex] x + -3
∴ y = [tex]\frac{-1}{2}[/tex] x - 3
∴ The equation of the perpendicular bisector is y = [tex]\frac{-1}{2}[/tex] x - 3
