How to rotate a triangle in an equation

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To rotate a triangle defined by specific equations around its centroid at (0,0), one must apply a rotation transformation to the coordinates. The correct method involves using rotation matrices rather than simple multiplication by cosine or sine, which would incorrectly scale the triangle. The rotation matrix for an angle θ is given by: cos(θ) -sin(θ) / sin(θ) cos(θ). Applying this matrix to each vertex of the triangle will achieve the desired rotation without altering its size. Properly implementing this transformation will allow for accurate rotation of the triangle around its centroid.
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Hi,

i have a set of definition for a triangle shape:

-3/4<x<3/4

-x/sqrt(3) + sqrt(3)/4 < y < x/sqrt(3) +sqrt(3)/4

The centroid of this triangle is at 0,0

i want to rotate this triangle by a certain degree from the centroid but i am not sure how, because if i just multiply it by cos or sin of the angle, it will just become smaller.

any hints will be appreciated.
 
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Any point can be rotated around the origin by rotating the coordinate system.
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