## Geometric Transformations within a Plane

#### Aligned To Common Core Standard:

**High School Congruence** - HSG-CO.A.2

What are Geometric Transformations within a Plane? What follows the images of the transformation that takes place on the plane. Originally the image is squared. The transformation image is shown, which undergoes transformation due to a function. A transformation on a plane is a function that maps points on a particular plane to other point or coordinates in the plane. In other words, a function that takes one point and puts it on another. For example, (a, b) to (c, d). A transformation is also called a function or mapping. When doing transformation on a plane, we start by imagining the image on that plane. For example, circles, lines, and curves, or any other type of figure. In this process, the image that exists before the transformation is called the pre-image, and the final picture is called the image. For example, if we have a function f [{x, y}]: = {x + 1, y +1 }. Then once the transformation is done, the image would have a radius 1 centered on (1, 1). This series of worksheets and lessons help students understand and classify the change of position of geometric shapes.

### Printable Worksheets And Lessons

- Triangle Shuffle Step-by-step
Lesson - This one is pretty basic. We move six steps laterally
and 2 steps vertically.

- Guided Lesson -
Here we work on rotations around the coordinate grid, simple translations,
and point translations.

- Guided Lesson Explanation
- It just struck me that I could have simplified things by added
arrows. On to the arrows.

- Practice Worksheet
- Three pages for students to work on independently.

- Matching Worksheet
- Make the new coordinates to the movements explained here.

- Transformations Five
Pack - Use the description of the triangle transformation to
draw the new triangle.

- Lines and Planes 5 Pack
- This is an advanced question set for your higher level learners.

- Triangle Transformations
Lesson and Practice - Anyone who has difficulty with this concept
should review this, it is very helpful.

#### Homework Sheets

You determine the coordinates of shapes after they have undergone a translation of some sort.

- Homework 1 - A translation slides a figure to a different location. Move point A(‐4, 1) right 4 units and down 1 unit. The new point A' is located at coordinates (0, 0).
- Homework 2 - Rotate point K(-6, 2) 90° counterclockwise around the origin. The point will move from Quadrant II to Quadrant III. The new point K' is located at (-2,-6).
- Homework 3 - Start with the point A (6, -6). Move the point 4 units left.

#### Practice Worksheets

I find that most kids have trouble understanding how objects translate up and to the left. Here you will find a bunch of practice questions on that specific topic.

- Practice 1 - Graph the image of D(6, 8) after a translation 7 units down.
- Practice 2 - Graph the image of rectangle PQR after a rotation 90° clockwise around the origin.
- Practice 3 - Write the coordinates of the vertices after a translation 3 units left and 3 units up.

#### Math Skill Quizzes

Filled with rotations and reflections across the axis.

### Why Is It Important to Be Able to Describe the Movement of Shapes and Objects?

It is often important to take a second and step back and evaluate why you are learning something. When it comes to learning to communicate a movement of something to another person, it is a vital skill. Regardless of the environment you are considering, being able to understand a location is key. Think about how integrated into our lives the GPS (Global Positioning System) is. We can barely travel around the block with out our mobile phones guiding our every step. GPS is merely an application of the type of math we are learning on the topic. While we really broke this concept down to the most primitive state, it is all not possible at all without addressing that fundamental concept. When you think about it, the applications of this foundation are limitless. It applies to anything that we are describing the movement of. The concept of the big three movements (rotations, reflections, and simple translations) are found in countless applications. All thanks to this basic concept.