To find the coordinates of point \( A \) (the pre-image) under a translation that moves point \( B \) (the image) to point \( C \), we need to know the translation vector. A translation can be expressed in terms of its vector, which shifts the coordinates by a certain amount in the x and y directions.
If you have the coordinates of point \( B \) (the image) and the translation vector \( \vec{v} = \langle v_x, v_y \rangle \), you can find the point \( A \) (the pre-image) by reversing the translation.
The formula for the coordinates of point \( A(x_A, y_A) \) would be:
\[ x_A = x_B - v_x \] \[ y_A = y_B - v_y \]
Replace \( x_B \) and \( y_B \) with the coordinates of point \( B \) and \( v_x \) and \( v_y \) with the components of the translation vector.
If you provide the coordinates of points \( B \) and the translation vector, I can calculate the coordinates of point \( A \) for you.