step 1
Find the equation of the line perpendicular to path A
Find the slope of path A
we need two points
(0,2) and (10,0)
m=(0-2)/(10-0)
m=-2/10
m=-1/5
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal
that means
the slope of the line perpendicular to path A is
m=5
Find the equation of the line in slope intercept form
y=mx+b
we have
point (0,2)
m=5
y=5x+2
step 2
Find the equation of the line perpendicular to path B
take the points (8,8) and (10,0)
m=(0-8)/(10-8)
m=-8/2
m=-4
the slope of the perpendicular line is
m=1/4
Find the equation of the line
we have
point (8,8)
m=1/4
8=(1/4)(8)+b
8=2+b
b=6
y=(1/4)x+6
step 3
Find the intersection point both lines
y=5x+2
y=(1/4)x+6
solve by graphing
see the attached figure
the coordinates are (0.842, 6.211)