Translations as Composition of Reflections
Any translation can be expressed as the composition of two reflections.
In the sketch below, A'B'C' is the result of translating ABC by vector v.
A''B''C''is the result of reflecting ABC over m then reflecting the image over n.
Play with the sketch (by moving the green points), and decide how to arrange the orange lines so thattriangle A''B''C'' coincides with A'B'C'.
What is the relationship among line m, line n, and the translation vector?