Translation as the composition of two axial symmetries

Any translation can be composed from two axial symmetries with parallel axes perpendicular to the direction of the translation, the distance of which is half the distance of the translation, and vice versa, composition of axial symmetries in two parallel lines is equal to a translation.

Task: Triangle A_tB_tC_t is an image of triangle ABC in the translation given by the vector t, see the red dashed oriented segment. Moving the axes o₁, o₂ (either directly with the lines or using points P₁, P₂, Q₁, Q₂), merge the yellow triangle A₂B₂C₂ with A_tB_tC_t.