Translation

Translation

Translation is a transformation which moves all points on a plane through the same direction. In the diagram, $\Delta ABC$ slides to $\Delta A'B'C'$ ($A'$ is read as A prime) in the direction $AA'$. Note that $AA'$ are parallel and of equal length. We say that $ABC$ is mapped onto $A'B'C'$ by a translation.

A translation is usually denoted by $T$. For example, $T(1, 1) = (6, 1)$ means that the point $(1,1)$ has been moved to $(6, 1)$ by a translation $T$. This translation will move the origin $(0,0)$ to $(5,0)$ and is written as $T = (5,0)$.

Translation drawings

If you cast a shadow of an object onto a plane surface, say a wall, by using a light source, the shadow becomes bigger as the object moves closer to the light source. In figure 7.40, $AB$ casts a shadow $CD$. When $AB$ moves to a new position and is renamed $QP$ (same size with $AB$) the shadow of $QP$ becomes $SR$ and it is greater than $CD$.