Plotting line perpendicular to another on the endpoint

Hello! I am looking to plot the perpendicular of my line at the endpoint of my line, forming a "T" shape.

My line starts at [0,0] and ends at [x,y] where

O = 0:pi/100:2*pi;
a = str2num(get(handles.Anibox,'String'));
n = str2num(get(handles.Numsides,'String'));
x = cos(O)+(a.*cos((n+1).*O));
y = sin(O)+(a.*sin((n+1).*O));

Is there a way to plot a line that is perpendicular to my line, and intersects at [x,y]?

also, would there be a way to control how long this line is?

Thank you for your help!

Answer 1

[Ryan Klots]

Note that any vector perpendicular to lies in the span of since . We can take advantage of this fact to construct the "T" bar.

Suppose we want each side of our "T" bar to have length r. We can constuct a vector of length r that is perpendicular to via the formula where is the norm of .

Then we can add this vector and its negative to in order to construct the endpoints of the "T" bar: