To find the perpendicular bisected of the line segment whose endpoints are (3,-7) (-9,-3).
We need to things:
1. the midpoint of the given point
2. the slope
The midpoint = p
[tex]p=\frac{(3,-7)+(-9,-3)}{2}=\frac{(-6,-10)}{2}=(-3,-5)[/tex]
To find the slope, first we will find the slope of the line segment whose endpoints are
(3,-7) (-9,-3)
so,
Slope = m = rise/run
Rise = -3 - (-7) = 4
Run = -9 - 3 = -12
Slope =
[tex]m=\frac{4}{-12}=-\frac{1}{3}[/tex]
The slope of the required line = m'
[tex]m^{\prime}=-\frac{1}{m}=-\frac{1}{\frac{-1}{3}}=3[/tex]
So, the equation of the line will be :
[tex]y=3x+b[/tex]
b is the y - intercept and will be calculated using the point p
when x = -3 , y = -5
so,
[tex]\begin{gathered} -5=3\cdot-3+b \\ -5=-9+b \\ b=-5+9 \\ b=4 \end{gathered}[/tex]
So, the equation for the perpendicular bisected is:
[tex]y=3x+4[/tex]
