How to find the point at which a line becomes perpendicular to another line?

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Cnell
Cnell 2020-7-29
评论： Cnell 2020-7-30
In the figure, the first two points are:
x = [150 0]
y = [0 150]
So, the line was plotted using
line(x,y,'color','red');
For a given red line, how can you find the point at which a line from the center becomes perpendicular to it? I just need the x value.
You can also think of it as the point where the radius value decreases then increases if you were to follow the red line from the first point to the second.

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KSSV
KSSV 2020-7-29
编辑：KSSV 2020-7-29
x = [150 0]
y = [0 150]
C = [0 0] ;
% get the line ax+by+c = 0
slope = diff(y)/diff(x) ; % slope
a = slope ;
b = -1 ;
c = y(1)-slope*x(1) ;
% foot of the perpendicular
m = -(a*C(1)+b*C(2)+c)/(a^2+b^2) ;
h = a*m+C(1) ;
k = b*m+C(2) ;
line(x,y,'color','red');
hold on
line([C(1) h],[C(2) k],'color','black')
line([h h],[k 0],'color','black')
plot(h,k,'*g')
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KSSV
KSSV 2020-7-30
This is not issue. This is correct. You need to extend the straight line..basic high school maths
% extend the straight line
x = 0:150 ;
y = -a/b*x-c/b ;
plot(x,y,'-b')

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