Transformations: Rotatations, Reflections, Translations

Transformations

> Definition
> Flip (Reflection)
> Slide (Translation)
> Turn (Rotation)

Students should be able to:

Predict and describe positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, and translations.

Definition

The word transform means "to change." In geometry, a transformation changes the position of a shape on a coordinate plane. What that really means is that a shape is moving from one place to another. There are three basic transformations:

Flip (Reflection)
Slide (Translation)
Turn (Rotation)

Being able to visualize the movement of a shape is very important. The SMARTBoard mini-movies below show a letter, or a polygon (after all, block letters are really just polygons), in their original positions before being transformed. By clicking the play button, we are able to watch the path the letter takes while being transformed and see their ending positions after the slide, flip, or turn has taken place.

Flip (Reflection)

A FLIP takes place when a shape is flipped across a line and faces the opposite direction. Because the shape ends up facing the opposite direction, it appears to be reflected, as in a mirror. Hence the name REFLECTION.

Click on the play button above to watch the letter N flip, or reflect. Click on the play button to watch it again.

Use this mini-movie on your Smartboard

Flip (Reflection)

A FLIP can also take place across a line in an up and down direction. In fact, a flip can take place in any direction. All you need to remember is the shape ends up facing the opposite direction and it appears to be reflected, as in a mirror. Hence the name REFLECTION.

Click on the play button above to watch the letter T flip, or reflect. Click on the play button to watch it again.

Slide (Translation)

A SLIDE takes place when a shape moves in one direction from one place to another. When you watch the shape move, it appears to be sliding. Often you will see an arrow underneath the shape to show what direction it is moving in.

Click on the play button above to watch the letter H slide, or translate. Click on the rewind button to watch it again.

Think About It

Look at the two H's above. Imagine you had not seen the slide take place and I told you that this was an example of a flip (reflection). Would this be true or false? (Click one of the buttons below)

Slide (Translation)

A letter can also SLIDE at an angle away from its original position. When you watch the W move, it appears to be sliding down and to the right. Notice it still looks exactly the same, just in a different position.

Click on the play button above to watch the letter W slide, or translate. Click on the rewind button to watch it again.

Turn (Rotation)

A letter can also turn on a point away from its original position. When you watch the T move, it turns, or rotates in place so that it now looks like it is laying on its side. It almost looks like a clock hand turning around the face of a clock.

Click on the play button above to watch the letter T turn, or rotate. Click on the rewind button to watch it again.

Turn (Rotation)

Now watch the letter A turn. When you watch the A move you'll notice that it moves from its original position, but still turns to its side. It also looks like a clock hand turning around the face of a clock.

Click on the play button above to watch the letter A turn, or rotate. Click on the rewind button to watch it again.

Now that you have seen the three types of transformations that shapes can undergo, it is time to test your knowledge. Click on the link below to take a quiz on transformations.