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Advanced Transformations


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Advanced Transformations

Students should be able to:

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



Pi link Pi link

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.


Check out the basic transformations page at:


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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.

A shape can reflect across the vertical axis, or y-axis, or it can reflect across the horizontal axis, or x-axis.

Click on the VERTICAL button to watch the letter N reflect over the vertical axis, or y-axis. Click the HORIZONTAL button to watch the letter N flip over the horizontal, or x-axis.



Slide (Translation)

A SLIDE, or TRANSLATION, 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 DIAGONAL button to watch the letter E translate in a diagonal direction. Click the HORIZONTAL button to watch the letter E translate in a horizontal direction.



Turn (Rotation)

A letter can also turn on a point away from its original position. It almost looks like a clock hand turning around the face of a clock. When you watch the A turn, or rotate, it will rotate by four different angles. When it rotates by 90, it looks like it is laying on its side. When it rotates by 180, it looks like it is upside down. When it rotates by 270, it also looks like it is lying on its side. A 360 rotation means the shape will turn all the around.

Click on each button to see how the A and/or the H will look after rotating by each angle.



Check out the basic transformations page at:








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