Translation
A translation in geometry is a transformation that slides a figure from one position to another without rotating it or flipping it. Every point in the figure moves the same distance in the same direction, so the shape and size remain identical — only the position changes. Translations are described by how many units a figure moves horizontally and vertically. For example, “translate 3 units right and 2 units down.” This concept is part of 7th grade geometry in Saxon Math, Course 2, and forms the basis for understanding rigid transformations.
Key Concepts
Property A translation 'slides' a figure to a new position without turning or flipping the figure.
Examples Translating rectangle $ABCD$ with vertex $A(2, 2)$ left 6 units and down 3 units moves $A$ to $A'( 4, 1)$. If point $P(0, 5)$ is translated right 2 units and up 1 unit, its new position is $P'(2, 6)$. To translate a point $(x, y)$ by $(a, b)$, the new coordinates are $(x+a, y+b)$.
Explanation A translation is like pushing a chess piece across the board. The shape doesn't twist, turn, or flip; it just glides to a new location. Every single point on the shape moves the exact same distance and in the exact same direction. It's a perfectly synchronized group trip for all the points!
Common Questions
What is a translation in geometry?
A translation is a transformation that moves every point of a figure the same distance in the same direction, essentially ‘sliding’ it to a new position without rotating or flipping it.
How does a translation change a figure?
A translation only changes the position of a figure. The size, shape, and orientation all remain exactly the same. It’s a rigid transformation — the figure doesn’t stretch or flip.
How do you describe a translation?
A translation is described by its direction and distance: ‘move 4 units right and 3 units up,’ or using coordinate notation like (x, y) → (x + 4, y + 3).
What is the difference between a translation, rotation, and reflection?
A translation slides a figure. A rotation turns it around a point. A reflection flips it over a line. All three are rigid transformations that preserve size and shape but change position or orientation.
What are the three rigid transformations?
The three rigid transformations (also called isometries) are translations (slides), rotations (turns), and reflections (flips). All three preserve the size and shape of the original figure.
When do students learn about translations?
Translations are introduced in 7th grade geometry as part of a unit on geometric transformations.
Which textbook covers translations?
Saxon Math, Course 2 covers translations as a type of geometric transformation.