Respuesta :
Given coordinates of the endpoints of a line segment (5,-9) and (1,3).
In order to find the equation of perpendicular line, we need to find the slope between given coordinates.
Slope between (5,-9) and (1,3) is :
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{3-\left(-9\right)}{1-5}[/tex]
[tex]m=-3[/tex]
Slope of the perpendicular line is reciprocal and opposite in sign.
Therefore, slope of the perpendicular line = 1/3.
Now, we need to find the midpoint of the given coordinates.
[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(\frac{1+5}{2},\:\frac{3-9}{2}\right)[/tex]
[tex]=\left(3,\:-3\right)[/tex]
Let us apply point-slope form of the linear equation:
y-y1 = m(x-x1)
y - (-3) = 1/3 (x - 3)
y +3 = 1/3 x - 1
Subtracting 3 from both sides, we get
y +3-3 = 1/3 x - 1 -3
