# How to rotate points on 2D coordinate systems

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Rightia Rollmann
on 5 Feb 2017

Commented: George Abrahams
on 12 Feb 2024

##### 0 Comments

### Accepted Answer

John Chilleri
on 6 Feb 2017

Hello,

Here's a simple implementation,

% Create rotation matrix

theta = 90; % to rotate 90 counterclockwise

R = [cosd(theta) -sind(theta); sind(theta) cosd(theta)];

% Rotate your point(s)

point = [3 5]'; % arbitrarily selected

rotpoint = R*point;

The rotpoint is the 90 degree counterclockwise rotated version of your original point.

Hope this helps!

##### 4 Comments

Ria
on 12 Feb 2024

Hello, if you needed the rotation clockwise, could you just reverse each sign of cosd and sind?

George Abrahams
on 12 Feb 2024

@Ria You have two options. First option, set theta, the angle of rotation, to -90. Second option, the inverse of a rotation matrix is its transpose, , so transpose the matrix. In MATLAB this is typically achieved with the .' syntax.

R = [cosd(-90) -sind(-90); sind(-90) cosd(-90)]

R = [cosd(90) -sind(90); sind(90) cosd(90)].'

### More Answers (3)

Amit
on 29 Mar 2023

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Amit
on 29 Mar 2023

Write the Matlab code for both the original parametric equation and computationally efficient parametric equation. Compare the computational times.

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Amit
on 29 Mar 2023

a) Write and execute a MATLAB program to plot a planar parametric curve whose x- and y- axis modeled using cubic polynomial of the form: X(u) =A*u^3+B*u+C Y(u) =E*u^3+F* u^2+G Where 0 ≤ u ≤ 1 is the parameter, and A, B, C, E, F, G are the polynomial coefficients. Your program should work for any user supplied input of these polynomial coefficients.

b) Write Matlab program to generate and plot a the Hermite cubic curve for any set of two control points and two tangent vectors. Validate your code with sample data given below: P0 = [1, 1], P’0 = [0.6, 0.8], P1= [8, 2] and P’1 = [-0.4472, -0.8944].

Also include in the program the facility of putting point at the specified u-value and an arrow for the tangent vector at that point.

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