Have you ever seen something that looked like this? Take a look at this dilemma.
This diagram represents a transformation. Do you know which one?
Pay attention and you will learn how to identify transformations like this one.
A transformation is the movement of a geometric figure on the coordinate plane.
There are several different types of transformations. One of these is called a translation. A translation is when a geometric figure slides up, down, left or right on the coordinate plane. The figure moves its location, but doesn’t change its position. It also doesn't change its size or shape.
Let's look at translations or slides.
When we perform translations, we slide a figure left or right, up or down. This means that, in the coordinate plane, the coordinates for the vertices of the figure will change.
We can represent this triangle by using coordinate notation. Coordinate notation is when we write ordered pairs to represent each of the vertices of a geometric figure that has been graphed on the coordinate plane.
These are the coordinates of the vertices of the triangle.
To graph a translation, we perform the same change for each point.
Now let's try graphing a translation. Take a look at this one.
Graph the following translation five places to the right.
Now you can see by looking at this square that there are four vertices, so there are four sets of ordered pairs to represent these vertices. Here are the ordered pairs.
Now let’s look at the graph of the translation.
Notice that while it is helpful to graph the square both first and then as a translation, it isn’t necessary to do so to figure out the coordinate notation. If you know the vertices of the figure that you are translating and you know how you are moving it, then you can figure out the new coordinates of the vertices.
Use this diagram to answer the following questions.
Is this figure a translation?
Solution: Yes, it shows a slide.
How many units up or down has the figure been moved?
Solution: Four units down or -4
How many units to the right or left?
Solution: Six units to the right or +6
Now let's go back to the dilemma from the beginning of the Concept.
Looking at this diagram, you can see that the figure, a quadrilateral has been shifted to the right and then up. It has not been flipped or turned. It has been moved, so this is a slide. Another name for a slide is a translation.
This is our answer.
moving a geometric figure on the coordinate plane.
using ordered pairs to represent the vertices of a figure that has been graphed on the coordinate plane.
A flip of a figure on the coordinate plane.
A slide – when a figure moves up, down, left or right on the coordinate plane, but does not change position.
Here is one for you to try on your own.
A triangle with the coordinates (0, 2), (2, 2) and (2, 5) is graphed on the coordinate grid. Find the coordinates of a translation moved three units down. Then graph the translation.
If we were to graph the translation, here is what we would see.
Transformation: Translation CK-12
Directions: Use the following diagram to answer each question.
1. What kind of transformation is shown in the diagram?
2. What are the coordinates of the first triangle?
3. What are the coordinates of the translated triangle?
4. What direction was the triangle first moved?
5. How many units?
6. Then which direction was the triangle moved?
7. How many units?
8. What are the coordinates of the first triangle?
9. What are the coordinates of the translated triangle?
10. Was the figure moved right or left?
11. How many units?
12. Was the figure moved up or down?
13. How many units?
14. True or false. Another name for a slide is a translation.
15. True or false. A rotation and a translation have the same characteristics.