Question: User: What is the translation
1. The question asks: What is the translation?
2. In mathematics, a translation is a type of transformation that slides every point of a figure or a space by the same distance in a given direction.
3. The formula for a translation in the coordinate plane is:
$$ (x, y) \to (x + a, y + b) $$
where $a$ is the horizontal shift and $b$ is the vertical shift.
4. This means every point $(x, y)$ moves to a new point $(x + a, y + b)$.
5. For example, if we translate a point $(3, 4)$ by $a = 2$ units right and $b = -1$ units down, the new point is:
$$ (3 + 2, 4 + (-1)) = (5, 3) $$
6. Translation does not change the shape or size of the figure, only its position.
Final answer: A translation moves every point of a figure by adding fixed amounts $a$ and $b$ to the $x$ and $y$ coordinates respectively.