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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 :
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.
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
<h3>y = 1/3 x - 4 .</h3>