## Dilations, Translations, Rotations, and Reflections

#### Aligned To Common Core Standard:

**Grade 8 Geometry** - 8.G.A.3

What are Dilations, Translations, Rotations, and Reflections?
In geometry, changing the position of a shape is referred to as transformation. Transformation is broadly broken into four types; dilation, translation, rotation, and reflections.
In some transformations, the position is changed but the size is maintained. Examples of this type of transformation are: translation, reflections, and rotations
In dilation, however, position and size both are altered.
Let's study each type briefly
**TRANSLATION** -
This type of transformation slides the figure through space or across a plane. All points that compose the figure move simultaneously to the same distance and travel in the same direction.
To simplify it for you, translation is the change in location, which is specified by a distance and a direction.
**ROTATION** -
Rotation, as the name implies, turns the figure around/about a line or point. It essentially spins the shape around. The point at which the figure is turned is known as the center of rotation. The center of rotation can be located inside or outside the shape.
Remember that rotation means to turn a figure about/ around
**REFLECTION** -
We have all studied reflection in science. Let's get familiar with its mathematical aspect.
In geometry, reflection means to transform a figure in a way that it is flipped across a line.
You might have noticed some figure that remains the same even if they are flipped over a line. This means that such figure can be folded along a line and have exactly same halves. Such shapes exhibit reflectional symmetry, and the line folding the paper is termed as a line of reflection.
**DILATION** -
Dilation retains the shape of the shape while altering the size of the shape. Dilation of a figure can be of two types; reduction and enlargement.
Enlargement means to increase the shape of the figure. While reduction means to decrease the size of the figure. The scale factor determines how much the size is reduced or enlarged.

### Printable Worksheets And Lessons

- Translating Points
Step-by-Step Lesson- Take a point. Move it around a grid system
based on directions.

- Guided Lesson
- This one really measures if you are paying attention to what you
read. I would advise you to read each question twice.

- Guided Lesson
Explanation -We work with flips and all kinds of other moves
across the board here.

- Independent Practice
- This one reminds me of the game battleship!

- Matching Worksheet - Some students find this a bit complicated. It does mirror question types that I have seen before on this skill.

#### Homework Sheets

Each sheet is focused on a specific type of transformation and offers you two visual problems.

- Homework 1 - What will be the coordinate if the point R (2,-2) is translated 3 units left?
- Homework 2 - If the point R (4, 3) is reflected over the y axis, what will be the coordinates of the resulting point, R’?
- Homework 3 - A reflection is also called a flip. It is to flip over the y-axis. The point is currently 4 unit away y-axis origin.

#### Practice Worksheets

We work with scale factors and point movements.

- Practice 1 - Graph the image of triangle ABC after dilation with the scale factor of 3, centered at the origin.
- Practice 2 - What will be the coordinates of the point Q' if the point Q(1, -3) is rotated 270˚ counterclockwise around the origin?
- Practice 3 - What will be the coordinate if the point H(-2, 2) is translated 5 units right?

#### Math Skill Quizzes

Time to play "What are the coordinates when point x is ..."

- Quiz 1 - What will be the coordinate if the point A (-1, 4) is translated 2 units left?
- Quiz 2 - If the point D(4, 4) is reflected over the y axis, what will be the coordinates of the resulting point,D'?
- Quiz 3 - Graph the image of parallelogram ABC after dilation with the scale factor of 2, centered at the origin.