1. Introduction
A figure is dilated if the preimage can be mapped to the image using a scale factor through a center point, usually the origin. You have been determining if figures have been dilated, but how do you create a dilation? If the dilation is centered about the origin, use the scale factor and multiply each coordinate in the figure by that scale factor. If a distance is given, multiply the distance by the scale factor.
1.1.2: Investigating Scale Factors

2. Key Concepts The notation is as follows: Dk(x, y) = (kx, ky).
Multiply each coordinate of the figure by the scale factor when the center is at (0, 0).
1.1.2: Investigating Scale Factors

3. Key Concepts, continued
1.1.2: Investigating Scale Factors

4. Key Concepts, continued
The lengths of each side in a figure also are multiplied by the scale factor.
If you know the lengths of the preimage figure and the scale factor, you can calculate the lengths of the image by multiplying the preimage lengths by the scale factor.
Remember that the dilation is an enlargement if k > 1, a reduction if 0 < k < 1, and a congruency transformation if k = 1.
1.1.2: Investigating Scale Factors

5. Common Errors/Misconceptions
not applying the scale factor to both the x- and y- coordinates in the point
improperly converting the decimal from a percentage
missing the connection between the scale factor and the ratio of the image lengths to the preimage lengths
1.1.2: Investigating Scale Factors

6. Guided Practice Example 2
A triangle has vertices G (2, –3), H (–6, 2), and J (0, 4). If the triangle is dilated by a scale factor of 0.5 through center C (0, 0), what are the image vertices? Draw the preimage and image on the coordinate plane.
1.1.2: Investigating Scale Factors

7. Guided Practice: Example 2, continued
Start with one vertex and multiply each coordinate by the scale factor, k.
Dk = (kx, ky)
1.1.2: Investigating Scale Factors

8. Guided Practice: Example 2, continued
Repeat the process with another vertex. Multiply each coordinate of the vertex by the scale factor.
1.1.2: Investigating Scale Factors

9. Guided Practice: Example 2, continued
Repeat the process for the last vertex. Multiply each coordinate of the vertex by the scale factor.
1.1.2: Investigating Scale Factors

10. Guided Practice: Example 2, continued List the image vertices.
1.1.2: Investigating Scale Factors

11. Guided Practice: Example 2, continued
Draw the preimage and image on the coordinate plane.
1.1.2: Investigating Scale Factors

12. Guided Practice: Example 2, continued✔
1.1.2: Investigating Scale Factors

13. Guided Practice: Example 2, continued
1.1.2: Investigating Scale Factors

14. Guided Practice Example 3
What are the side lengths of with a scale factor of 2.5 given the preimage and image to the right and the information that DE = 1, EF = 9.2, and FD = 8.6?
1.1.2: Investigating Scale Factors

15. Guided Practice: Example 3, continued
Choose a side to start with and multiply the scale factor (k) by that side length.
1.1.2: Investigating Scale Factors

16. Guided Practice: Example 3, continued
Choose a second side and multiply the scale factor by that side length.
1.1.2: Investigating Scale Factors

17. Guided Practice: Example 3, continued
Choose the last side and multiply the scale factor by that side length.
1.1.2: Investigating Scale Factors

18. Guided Practice: Example 3, continued
Label the figure with the side lengths.
1.1.2: Investigating Scale Factors

19. Guided Practice: Example 3, continued✔
1.1.2: Investigating Scale Factors

20. Guided Practice: Example 3, continued
1.1.2: Investigating Scale Factors