how to move point along line with specific direction

Hi I have the folowing image:

As seen in the image, the points are randomly distributed in the x-y plane.Each point has its own x any y local axis. I need to move the red point a long its x-axis, how I can do that? I know the coordinates of the red point and the direction of x-axis (the angle in radian).here the code for drawing the points and the directions for each point: function [ h, xEnd, yEnd ] = draw_arena( x, y, theta, a, b )

L = 2;                              %# Length of arrow
s = 0.2;                            %# stretch o the arrow
xEnd = L*cos(theta);                %# X component of the x_axis arrow
yEnd = L*sin(theta);                %# Y component of arrow of the x_axis
hold on;                            %# Add subsequent plots to the current axes
axis ([a b a b])                    %# Set axis limits
axis equal;                         %# Make tick increments of each axis equal
for i = 1:length(x)
  h(i) = plot(x(i),y(i),'o','MarkerEdgeColor','b','MarkerFaceColor','b','Markersize',20);  %# Plot the points
end    
x_axis = quiver(x,y,xEnd,yEnd,s,'color',[1 1 0]);  %# plot yellow  x-axis
text((x+xEnd),(y+yEnd),'x')
x_End = L*cos(theta+ pi/2);         %#  X component of the y_axis arrow end
y_End = L*sin(theta + pi/2);        %# Y component of arrow of the y_axis end
y_axis=quiver(x,y,x_End,y_End,s,'color',[1 0 1]);   %# plot purple y_axis
text((x+x_End),(y+y_End),'y')
end

I would appreciate your help I would like also to rotate the x-axis for the blue points, so that they align with the red point x-axis?I required to find the coordinates of the blue points in term of red point coordinates I know the distance between points and have the angle between each point x-axis and the standard (common) x-axis. How I can do that rotation? how I can find the angle between each point x-axis and the red point x-axis and the points value in using the red point coordinates? Thanks for your help

[Eman hasan]

I would like also to rotate the x-axis for the blue points, so that they align with the red point x-axis?I required to find the coordinates of the blue points in term of red point coordinates I know the distance between points and have the angle between each point x-axis and the standard (common) x-axis. How I can do that rotation? how I can find the angle between each point x-axis and the red point x-axis and the points value in using the red point coordinates? Thanks for your help

Answer 1

[Walter Roberson]

See animatedline()

[Eman hasan]

thanks, it works now