# Transformations Manipulative

A transformation manipulative is an example of something that workds better as a virtual manipulative than a physical manipulative. Geoboards are often used to teach transformations, but manipulating geoboard rubber bands can be cumbersome. Additionally, while geoboards can be used to perform translations, reflections, and dilations, they are not very effective for performing rotations.

Virtual Transformations Manipulative

Virtual manipulatives, such as Brainingcamp's Transformations Manipulative, take advantage of a virtual environment to let student perform transformations that are difficult or impossible in the real world. Users can place 1- to 6-vertex objects and easily manpulate shapes by moving vertices. Translations are performed by dragging an image. Rotations are performed by spinning an image around a customizable center of rotation. Lines of reflections can easily be moved and rotated. Dilations are performed by dragging an image toward or away from a customizable center of rotation.

Using Transformations Manipulative

Translations

A translation is like a slide where every point of the preimage is moved by the same distance, in the same direction. Translate a preimage and notice that the image and preimage have the same shape and size.

Reflections

A reflection is a mirror-image flip over a line called the "line of reflection". Reflect an image. Corresponding points on the image and preimage are the same distance from the line of reflection. To reflect over the x-axis, multiply the y-coordinate by -1. To reflect over the y-axis, multiply the x-coordinate by -1. Notice that the image and preimage have the same shape and size.

Rotations

A rotation turns a figure about a point called the center of rotation. Rotate an image. Corresponding points on the image and preimage are the same distance from the center of rotation. Notice that the image and preimage have the same shape and size.

Dilations

A dilation enlarges or reduces a figure by a scale factor relative to a point called the center point. Dilate an image. Each point on the preimage can be multiplied but the scale factor to find the corresponding point on the image. Notice that the image and preimage have the same shape, but not necessarily the same size. The scale produces a reduction when less than 1, an enlargement when greater than 1, and no change when equal to 1.

Congruence

Two figures are congruent if one can be obtained from the other by a sequence of translations, reflections, and rotations. Congruent figures have the same shape and the same size. The Brainingcamp Transformations Manipulative has a Congruence mode where two congruent figures have different initial orientations. Users can perform a sequence of translations, rotations, and reflections to exactly fit the one figure on top of the other.

Similarity

Two figures are similar if one can be obtained from the other by a sequence of translations, reflections, and rotations. Congruent figures have the same shape and the same size. The Brainingcamp Transformations Manipulative has a Similarity mode where two similar figures have different initial orientations. Users can perform a sequence of translations, rotations, and reflections to fit the one figure over the other such that the figures have the same orientation. Users will then see that the figures have the same shape, but not necessarily the same size.

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