Translation
Translation is a Grade 8 geometry transformation in Saxon Math Course 3, Chapter 3, where every point of a figure is moved the same distance and direction without rotating, reflecting, or resizing. Students describe translations using coordinate notation, apply translation rules to move figures on the coordinate plane, and confirm that the image is congruent to the original.
Key Concepts
Property A translation is a 'slide.' It moves a figure a specific distance and direction without any turning or flipping. For a translation $(a, b)$, 'a' is the horizontal shift and 'b' is the vertical shift.
Examples Applying a translation of $(6, 2)$ to a point at $( 1, 4)$ moves it to a new location at $( 1+6, 4+2)$, which is $(5, 6)$. A square with vertices at $(0,0), (3,0), (3,3), (0,3)$ translated by $( 4, 2)$ moves to new vertices at $( 4, 2), ( 1, 2), ( 1,1), ( 4,1)$.
Explanation This is the simplest move! A translation just slides an object from one spot to another. Think about moving a game piece on a board—it doesn’t turn or flip, it just glides across. The translation vector, like $(5, 3)$, gives you the secret directions: move 5 units right and 3 units down to find the new location.
Common Questions
What is a translation in geometry?
A translation is a transformation that slides every point of a figure the same distance in the same direction without rotating or reflecting it. The resulting image is congruent to the original.
How do you describe a translation on the coordinate plane?
Describe it as moving a number of units right or left (horizontal shift) and up or down (vertical shift). This is written as (x + a, y + b) where a is the horizontal shift and b is the vertical shift.
How does a translation affect the coordinates of a point?
Add the horizontal shift to the x-coordinate and the vertical shift to the y-coordinate. For example, translating the point (2, 3) by (4, -1) gives (6, 2).
Does translation change the size or shape of a figure?
No. Translation is a rigid transformation that preserves both the size and shape of the figure. The translated image is congruent to the original.
Where is translation taught in Grade 8?
Translation is covered in Saxon Math Course 3, Chapter 3: Number and Operations.