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Dilations and Scale Factors

Answer Keys Here

Aligned To Common Core Standard:

Trigonometry - HSG-SRT.A.1b

What are Scale Factors? Playing with objects is fun, right? Sometimes you want to make an object smaller than it originally is, sometimes larger. Like how easy it is to fold and unfold clothes. We shrink them to fix them in a small area and open them to fit on our bodies. Fun, right? Just like that, number dimensions can also be switched to make shapes bigger or smaller. A number used for multiplying dimensions to get another shape that looks exactly the same but is either bigger or smaller is known is Scale Factor. Let's take an example that you have a square with a measurement of one foot on each side. To make it bigger, we will use the scale factor of two, so each side of the square will be multiplied by two. This will make the square bigger, and now it will have measurements of two-foot. Now let's say we have a triangle that is two-inch in height and one inch in its width. We will use the scale factor of 1/2 to make the triangle smaller than it's the original shape. Now, the triangle would be one inch high and 0.5 inches long.

Printable Worksheets And Lessons

Homework Sheets

Show us how the shape is changed on a coordinate system based on the dilation.

  • Homework 1 - This dilation is centered at the origin, so you can find the image by multiplying the x- and y-coordinates by the scale factor.
  • Homework 2 - Multiply the coordinates of point A(-8, -12) by 1/4. The image is A'(-2,-3).
  • Homework 3 - The movement here is pretty substantial.

Practice Worksheets

The reason I made these so large is so that students have no trouble seeing the exact coordinates.

  • Practice 1 - Graph the image of rectangle ABCD after dilation with a scale factor of 1/4, centered at the origin.
  • Practice 2 - See if you can breakdown the scale factor in this one.
  • Practice 3 - Where does this one move about?

Math Skill Quizzes

I through a number of fun images here, just to lock down the concept.

  • Quiz 1 - True or false, the images display dilation?
  • Quiz 2 - See if these are shiny.
  • Quiz 3 - See if you remember number 2?