1. Notes Dilations

2. Definitions
Dilation - a transformation in which every point P has an image P' placed on OP so that
and OP' = k * OP
Center of Dilation – the point from which an original figure is dilated.
Scale Factor - the ratio of the image length to the corresponding original length.

3. Scale Factor
If the scaled factor is greater than 1, then it is an enlargement (k>1).
If the scaled factor is equal to 1, then it is a congruent figure (k=1)
If the scale factor is less than 1, then it is a reduction (k<1).

4. This dilation is an enlargement . Corresponding distances
Image Distance 4 2
= = 2
= k
Scale Factor
Original Distance
2 > 1
This dilation is an enlargement .
Corresponding distances

5. This dilation is an reduction. Corresponding distances
Image Distance 2 3 =
= k
Scale Factor
Original Distance
2/3 < 1
This dilation is an reduction.
Corresponding distances

6. Example:
Rectangle W’X’Y’Z’ is the image of rectangle WXYZ after a dilation.
Find the scale factor of the dilation.
Tell whether the image is a reduction or an enlargement.

7. Example: 2.

8. Example: 3.

9. Reduction, Enlargement, or Congruent?
K = 4
K = ½
K = 1
4>1 Enlargement
½ <1 Reduction
Congruent

10. Matching K = ¼ K = 3 Reduction K = 2/7 Enlargement K = 1 K = 5
Congruent

11. 7. scale factor 2

12. 8. scale factor ¼

13. 8. scale factor 1/3