equation for the perpendicular Bisector of the line segment whose endpoints are (-9,-8) and (7,-4)
Perpendicular bisector lies at the midpoint of a line
Lets find mid point of (-9,-8) and (7,-4)
midpoint formula is
[tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex]
[tex]\frac{-9+7}{2} ,\frac{-8+-4}{2}[/tex]
midpoint is (-1, -6)
Now find the slope of the given line
(-9,-8) and (7,-4)
[tex]slope = \frac{y2-y1}{x2-x1} = \frac{-4-(-8)}{7-(-9)}[/tex]
[tex]slope = \frac{-4+8}{7+9}= \frac{4}{16} =\frac{1}{4}[/tex]
Slope of perpendicular line is negative reciprocal of slope of given line
So slope of perpendicular line is -4
slope = -4 and midpoint is (-1,-6)
y - y1 = m(x-x1)
y - (-6) = -4(x-(-1))
y + 6 = -4(x+1)
y + 6 = -4x -4
Subtract 6 on both sides
y = -4x -4-6
y= -4x -10
equation for the perpendicular Bisector y = -4x - 10
