9.7 Dilations/7.2 Similarity Transformations

Warm Up: Find the image point when the indicated transformation is applied to the given preimage point.

1. (x, y) (x + 3, y – 1); (2, 4) 2. (x, y) (x, -y); (-2, 1)

3. (x, y) (3x, 3y); (-5, 0) 4. (x, y) ( ,x y1 1

3 3); (3, -6)

Dilation:

Make a conjecture! What do you think the scale factors below will do to the figures?

Scale Factor of 2 Scale Factor of ½ Scale Factor of -2 Scale Factor of -½ Investigate! Draw each figure with the given vertices and its image under a dilation with the given scale factor centered at the origin.

5. J(1, 3), K(2,1), L(3, 4); scale factor: 2 6. A(0, 0), B(2, 6), C(6, 4); scale factor: 1

2

.

7. R(1, 0), S(1, -2), T(-1, -2); scale factor: -2 8. G(2, 0), H(0, 4), I(4, 2); scale factor: 1

-2

Was your conjecture correct? Use your investigation to help you come up with a rule for each scale factor

Tell whether each transformation appears to be a dilation. Explain.

9. 10. 11. 12.

Applications: 13. An artist is creating a large painting from a photograph by dividing the photo into squares and dilating each square by a scale factor of 4. If the photograph is 20 cm by 25 cm, what is the perimeter of the paining?

14. An engraver is designing a stamp to celebrate Asian American history. Her original version of the

stamp is a rectangle 6 inches by 9 inches. When the stamp is produced, it will be a rectangle 1 inch by 1.5

inches. Find the scale factor of the reduction.

15. A sign painter creates a rectangular sign for Mom’s Diner on his computer desktop. The desktop

version is 12 inches by 4 inches. The actual sign will be 15 feet by 5 feet. If the capital M in “Mom’s” will

be 4 feet tall, find the height of the M on his desktop version.

Scale Factor k

K > 1 0 < K < 1 -1 < K < 0 K < -1