The equation of the line is:
y-yo = m (x-xo)
Where,
m = (y2-y1) / (x2-x1)
Substituting values:
m = (8-4) / (6-2)
m = (4) / (4)
m = 1
Then, the equation is:
y-4 = 1 * (x-2)
Rewriting:
y = x-2 + 4
y = x + 2
The midpoint is:
k = ((x1 + x2) / 2, (y1 + y2) / 2)
k = ((2 + 6) / 2, (4 + 8) / 2)
k = ((8) / 2, (12) / 2)
k = (4, 6)
Then, the equation of the perpendicular line that passes through k is:
y = -x + b
Looking for b we have:
6 = -4 + b
b = 6 + 4
b = 10
Substituting:
y = -x + 10
Answer:
An equation of a line perpendicular to jl and passing through k is:
y = -x + 10
