## Properties of Rotations, Reflections, and Translations

#### Aligned To Common Core Standard:

**Grade 8 Geometry** - 8.G.A.1

Common Properties of Rotations, Reflections, and Translations
**Rotations** - Have you ever turned the handle of a door? The action that you performed is called rotation. In math, rotation is the same! In simple words, rotation is anything that changes its position around a fixed axis or point.
- Rotation moves line to line, segment to segment, rays to rays, angles to angles, parallel lines to parallel lines
- Rotation preserves the segment's length and degrees to the measure of an angle is similar to the translation.
- Rotation requires more than one piece of information
**Translations** - When you slide something across the table, then it means that you have performed an action that is called translation. In the process of translation of an object along (x,y) coordinates, one of the axes will remain constant. For example, shifting books on a bookshelf 18 inches to the left. As the movement is horizontal, the y-axis will remain constant.
**Reflection** - As the name suggests, it is a movement that causes the shape of an object to flip across the same line. It is the same process that is caused by the mirror. The shape is drawn usually on a 2D coordinate (x,y)
These worksheets and lessons have students reflect, rotate, and translate objects, shapes, and points using a coordinate grid system.

### Printable Worksheets And Lessons

- Translation Step-by-Step
Lesson- We use graphing talk to get this one to translate across
the axis.

- Guided Lesson
- We cover all three skills of this section: Reflection, Rotation,
and Translation.

- Guided Lesson Explanation
- The explanations are a bit lengthy to cover the concepts in detail.

- Independent Practice
- This one is pretty quick, once you get the hang of it.

- Matching Worksheet
- Did the colored points give it away? I guess so. I use this one
for practice with my students.

- Transformations Five
Pack - Some of these images make it really tough to determine
the outcome.

- Identify Line Reflection
Five Pack - Are you seeing a slide, flip, or turn?

- Exploring Similar Figures
Five Pack - Are you seeing a reflection?

- Reflection in a Line Worksheet
Five Pack - It is all about tracking the movements of a point.

- Reflection in a Line Worksheet
Five Pack Version 2 - More of the same here.

- Reflection in a Point Worksheet
Five Pack - Describe what the reflections should look like.

- Reflection in a Point Worksheet Five Pack Version 2 - Find the image of the point.

#### Homework Sheets

Time to jump our points all over the place.

- Homework 1 - Graph the image of B(3, 3) after a translation 4 units down. First we have to start with the point B (3, 3). Then we should move 4 units down.
- Homework 2 - Reflections are a transformation where one figure is the mirror image of another.
- Homework 3 - We also know that 180° is 1/2 of a full turn. So, the rotation will turn the point 1/2 of a full turn in the clockwise direction.

#### Practice Worksheets

We focus on one of the major topics on each sheet.

- Practice 1 - Graph the image of P (-6, 4) after a reflection over the y-axis.
- Practice 2 - Graph the image of N (10, 10) after a rotation 270°counter clockwise around the origin.
- Practice 3 - Graph the image of R (-40, -40) after a reflection over the x-axis.

#### Math Skill Quizzes

It's best to sketch what each question is asking you before you actually plot the points.