## Dilations and Parallel Lines

#### Aligned To Common Core Standard:

**Trigonometry** - HSG-SRT.A.1a

What are Geometric Dilations? We know what the basic geometrical terms are, right? Lines, segments, shapes, figures. Let's take a look at something new today. Have you heard about geometric dilations? Let's understand what they are! A transformation that can change the length of all line segments by the same proportion is known as dilation. Dilations do not change figures; they change the size. In very simple words, when talking geometrically, dilations refer to making something change its sizes. The shape of the figure is not altered, only the sizes are changed i-e: the images can become either bigger or smaller. For completing a dilation, two things are needed. A fixed point or center point and scale factor or ratio. If the absolute value of the scale factor is less than 1, then the image is small and if the value is greater than 1, then the image will be large. These worksheets and lessons help students learn how to go about dilating a line in several situations.

### Printable Worksheets And Lessons

- Write the Equation
Step-by-step Lesson - We pack you in here to rewrite an equation
of the line after a dilation.

- Guided Lesson
- This lesson can take some kids half an hour to manage properly.

- Guided Lesson Explanation
- These problems took me about 2 hours to explain properly, see
if it worked out.

- Practice Worksheet
- Scale factors come into play here to work the line.

- Matching Worksheet
- This could take an hour or so to complete.

#### Homework Sheets

It is all about writing the equation for the lines and making adjustments.

- Homework 1 - In most circumstances it is best to start with the y-intercept.
- Homework 2 - Write your answer in slope-intercept form.
- Homework 3 - Where is the origin in reference to the line?

#### Practice Worksheets

Scale factors tend to throw kids for a loop. Help center them on the concept.

- Practice 1 - Write the equation of the image of l after dilation with a scale factor of 4, centered at the origin.
- Practice 2 - Use the graph to get a visual understanding of the system for yourself.
- Practice 3 - This line strikes the origin.

#### Math Skill Quizzes

The quizzes build in a progression. They are much easier to work on in order.