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

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.

[KSSV]

Read about foot of te perpendicular.

Answer 1

[KSSV]

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')

[Cnell]

Very clever! I need it to work for any x and y though

[KSSV]

Replace C with your (x,y). Simple.

[Cnell]

C should always be [0 0]. Could you clarify bc I am having issues with the points

x = [150 50]
y = [0 50]

[KSSV]

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')

[Cnell]

Actually, it was the scaling of the plot :)