Translation of a triangle in xy plane by moving its centroid

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thanks for taking your time to read my question

Consider this problem. Let's say I have three points

A(x1,y1), B(x2,y2) and C(x3,y3).

The centroid of the triangle formed by these three points has the following coordinates:

$ x_c = {x_1 + x_2 + x_3\over 3}, y_c = {y_1 + y_2 + y_3\over 3} $

Now, if I am given a point say with the coordinates $x_{c1}, y_{c1}$

I have to perform the translation of my triangle by moving the centroid of the triangle, so that the centroid of the translated triangle is at the point $ x_c = {x_1 + x_2 + x_3\over 3}, y_c = {y_1 + y_2 + y_3\over 3} $

How can I determine the coordinates of the vertices of the new triangle? I am completely stuck on this.

Thanks for helping!