Lesson 23 — Activity 2: What Are Translations?
Completion requirements
Lesson 23 — Activity 2:
What Are Translations?
Lesson 23 — Activity 2:
What Are Translations?
A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction.
The word translate in Latin means "carried across."
In geometry, "translation" simply means "moving."
When you are sliding down a waterslide, you are experiencing a translation. Your body is moving a given distance (the
length of the slide) in a given direction. You do not change your size, shape, or the direction in which you are facing.
A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction.
The word translate in Latin means "carried across." In geometry, "translation" simply means "moving."
When you are sliding down a waterslide, you are experiencing a translation. Your body is moving a given distance (the length of the slide) in a given direction. You do not change your size, shape, or the direction in which you are facing.
The word translate in Latin means "carried across." In geometry, "translation" simply means "moving."
When you are sliding down a waterslide, you are experiencing a translation. Your body is moving a given distance (the length of the slide) in a given direction. You do not change your size, shape, or the direction in which you are facing.
Some examples of where you might see translations occurring in everyday life include: wallpaper designs, textile patterns, mosaics, and artwork.
Image Source: Pexels
Translations shown in textile designs.
Image Source: Pexels
Translations shown in a mosaic.
Translations can also be seen in architectural designs. All the stadium seats in this photograph are the same size and shape and face in the same direction.
Image Source: Pexels
Translations shown in textile designs.
Image Source: Pexels
Translations shown in a mosaic.
Image Source: Pixabay
Musicians use translations when they compose musical scores. Certain patterns of musical notes are often repeated within a composition. Think of songs you know where a certain phrase or sequence repeats.
To translate a shape, every point of the shape must move:
- the same distance
- the same direction
Click on the Play button below to watch a video on translations.
The figure below is an example of a translation using shapes.
The translation moves the shape 6 to the right and 3 down.
To complete this task, every point on the figure must be moved (or slid) in that exact direction.
Let's take a look at another example.
Create the following translation:
(
x, y) → (x – 5, y+1)
Hint: This means subtract 5 from each of the x-coordinates and add 1 to each of the y coordinates.
To complete this task, you must identify each point of the triangle, and then insert it into the equations for x and y.
In the new shape location, the triangle has been moved 5 to the left and 1 up.
Self-check!
Try This!
The triangle below slides to a new position.
Which of the following could be the new position of the triangle?
