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## Graphing Complex Transformations

#### High School Congruence - HSG-CO.A.3

What are Complex Transformations in Geometry? Many students struggle with the complex transformations that take place in geometry. For functions that include real variable such as f(x) = sin x, g(x) = x2 + 2 etc. you are used to illustrating these transformations geometrically and usually on a cartesian coordinate system. If the functions that are involved have complex variables such as w = sin z or w = z2 +2, it is not possible to make a cartesian graph because z cannot be represented on an x, y plane system. It would be difficult to visualize this on a cartesian system, and therefore, we need to make two copies of the complex plane and then look at the points that are made on the z-plane and see how they are being transformed into the points on w-plane. Example: w = f(z) = z + 2. This simply shifts every single point two units in the direction of the real axis - which is called a translation. These worksheets and lessons help students learn and experiment with the movement of common transformations.

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

Understanding the vocabulary for this section is paramount.

• Homework 1 - Write the coordinates of the vertices after a translation and rotation. Graph the image of ABC after the following transformations: Translation (x, y) (x + 5, y + 4) Rotation 270° counterclockwise around the origin.
• Homework 2 - Graph the image of PQRS after the following transformations: Translation (x, y) (x - 3, y + 3)
• Homework 3 - Use the transformation rule (x, y) (x-3, y+5) to find the image of each of its three vertices.

#### Practice Worksheets

I would go over the transformation rules and scales with students first before working on these.

• Practice 1 - Graph the image of PQRS after the following transformations: Translation (x, y) ----> (x – 1, y + 2).
• Practice 2 - Graph the image of XYZ after the translation.
• Practice 3 - Graph the image of STV after the following transformations: Rotation 270° counterclockwise around the origin.

#### Math Skill Quizzes

Quiz 1 and 3 are very traditional. The second quiz is me trying to adapt the skill to the real world.

• Quiz 1 - Process a translation and then rotation.
• Quiz 2 - What is the measure of the angle tip of the crayons with the line?
• Quiz 3 - Is the rotation counterclockwise?