Rotation of an xy coordinate system

Hi fellow MatLabbers, this is my first post. I hope I hang around here and ask questions and hopefully answer some at some point.

So... My first post question is:

I have a triangle with vectors (1,0) (2,4) and (-2,2) and I am supposed to rotate it by 2pi/3 in respect to the ORIGIN. Then I need to calculate the new coordinates after the rotation. Then I need to plot both the original and rotated triangle. This is what I have so far:

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clear all
x = [1 2 -2 1];
y = [0 4 2 0];
theta = (2*pi)/3;
v=[x;y];
R = [cos(theta) sin(theta); -sin(theta) cos(theta)];
so = R*v;  
x_rotated = so(1,:);
y_rotated = so(2,:);
% make a plot
plot(x, y, 'k-', x_rotated, y_rotated);
axis equal

x_rotated

x_rotated = 1×4

-0.5000 2.4641 2.7321 -0.5000

y_rotated

y_rotated = 1×4

-0.8660 -3.7321 0.7321 -0.8660

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I am not entirely sure if my result is correct because I assume since it needs to rotate in respect to the origin, the first vector should? stay the same.

Answer 1

[Matt J]

Looks fine to me. When you rotate about the origin, the only point that stays fixed is the origin.

[xRah]

But isn't the origin supposed to be the first vertex (and last)?

[Matt J]

The origin is the point x,y=(0,0). None of your vertices are located there.

[xRah]

Thanks for your input. I will accept your reply as answer soon if nobody objects :) I appreciate your help.