Home > Grade Levels > High School Geometry >

## Drawing Transformed Figures

#### High School Congruence - HSG-CO.A.5

What are Transformed Figures in Geometry? In geometry, transformed figures are those that have been moved from their original position on the coordinate system. There are four common types of transformations and two definitions of transformation. Definition of Transformations - Geometric transformations, in general, involve taking preimage and transforming that later into some form of an image. The definition falls under two different categories: Rigid Transformation - In a rigid transformation, the shape and size of the preimage don't change at all. Non-Rigid Transformation - In Non-Rigid Transformation, the size will change, but the preimage shape will remain the same. Types of Transformations - Within the two categories that have been mentioned above, there are four main types of categories of transformations, out of which, three falls under the category of rigid transformation and one under non-rigid. 1. Rotation: When an object is rotated from its fixed point without any change in shape or size. 2. Translation: Moving an object within the space without causing any change in the orientation, shape or size. 3. Dilation: contracting or expanding an object without changing its shape or size. 4. Reflection: when the object is flipped across a line without any change in shape or size. This collection of worksheets and lessons teach students how to create transformed geometric shapes.

### Printable Worksheets And Lessons  #### Homework Sheets

We get a bit extreme with translating points all across the coordinate plane.

• Homework 1 - A rotation turns a figure around a fixed point. 90° is 1/4 of a full turn. The rotation will turn the point 1/4 of a full turn in the clockwise direction. It looks like the diagram below if we are rotating about the origin.
• Homework 2 - A reflection flips the figure over a line to create a mirror image. A rotation turns the figure around a point. A translation slides the figure to a different location.
• Homework 3 - A glide reflection is the composition of a translation followed by a reflection across a line parallel to the direction of the translation. The image of a point (x,y) reflected across the xaxis is (x, y).

#### Practice Worksheets

Some of these will take you a good bit of time to size up.

• Practice 1 - Graph the image of B (35, -7) after a rotation 180o counterclockwise around the origin.
• Practice 2 - Which image shows a reflection of this shape?
• Practice 3 - Graph the image of ABCD after the following glide reflection: Translation (x, y) -> (x+9, y). Reflection across the x-axis.

#### Math Skill Quizzes

We move shapes and points all over the graph again.

• Quiz 1 - This focuses on the use of glides.
• Quiz 2 - This quiz hones in on the rotation around the origin.
• Quiz 3 - A reflection focused quiz.