Question

Find an equation for the perpendicular Bisector of the line segment whose endpoints are (-9,-8) and (7,-4

Answer 1

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

$\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}$

$\frac{-9+7}{2} ,\frac{-8+-4}{2}$

midpoint is (-1, -6)

Now find the slope of the given line

(-9,-8) and (7,-4)

$slope = \frac{y2-y1}{x2-x1} = \frac{-4-(-8)}{7-(-9)}$

$slope = \frac{-4+8}{7+9}= \frac{4}{16} =\frac{1}{4}$

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