1. 12.7 Dilations

2. Dilations
Dilation: A transformation that changes the size of a figure, but not the shape.
The image and the preimage are similar

3. Examples:
Tell whether each transformation appears to b a dilation. Explain.

4. Examples:
Tell whether each transformation appears to be a dilation. Explain.

5. Dilations:
For a dilation with scale factor k, if k > 0, the figure is not turned or flipped. If k < 0, the figure is rotated by 180°.

6. Dilations:

7. Enlargements/Reductions
Enlargement: (expansions) enlarges all dimensions proportionally. A dilation with a scale factor greater than 1.
Reduction: (contraction) reduces all dimensions proportionally. A dilation with a scale factor greater than 0, but less than 1.

8. Examples:
On a sketch of a flower, 4 in. represent 1 in. on the actual flower. If the flower has a 3 in. diameter in the sketch, find the diameter of the actual flower.

9. Examples:
An artist is creating a large painting from a photograph into square and dilating each square by a factor of 4. Suppose the photograph is a square with sides of length 10 in. Find the area of the painting.

10. Dilations In The Coordinate Plane

11. Negative Dilations
If the scale factor of a dilation is negative, the preimage is rotated by 180°.

12. Examples:
Draw the image of the triangle with vertices P(-4, 4), Q(-2, -2), and R(4, 0) under a dilation with a scale factor of
centered at the origin.

13. Examples:
Draw the image of the triangle with vertices R(0, 0), S(4, 0), T(2, -2), and U(–2, –2) under a dilation centered at the origin with a scale factor of

14. Examples:
A rectangle on a transparency has length 6 cm and width. On the transparency 1 cm represents 12 cm on the projection. Find the perimeter of the rectangle in the projection.

15. Examples:
Draw the image of the triangle with vertices E(2, 1), F (1, 2) and G(-2, 2) under a dilation with a scale factor of -2 centered at the origin.