Answer:
The equation of perpendicular bisector is:
[tex]y = 2x-2[/tex]
Step-by-step explanation:
Given the points
First, we need to find the midpoint of the points (-4, 3) and (8, -3)
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]
[tex]=\left(\frac{8-4}{2},\:\frac{-3+3}{2}\right)[/tex]
[tex]=\left(2,\:0\right)[/tex]
Thus, the midpoint of the points is: (2, 0)
Now, finding the slope between (-4, 3) and (8, -3)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]
[tex]m=-\frac{1}{2}[/tex]
Therefore, the slope m = -1/2
The slope of the line perpendicular to the segment = [-1] / [-1/2] = 2
Using the point-slope form of the equation of the line, the equation of perpendicular bisector is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line
substituting the slope 2 and the point (2, 0)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - 0 = 2 (x-2)[/tex]
[tex]y = 2x-2[/tex]
Therefore, the equation of perpendicular bisector is:
[tex]y = 2x-2[/tex]
