Aim:______________________________________________________________________________________

_____________________________: a transformation that _____________________________ or

___________________________ the distance between each point in a figure from the center of dilation.

________________________________________________: the multiple by which a dilation changes size.

A _______________________ creates a __________________ figure with side lengths that are

__________________________.

Angle measures ________________________________________________!

A dilation results in a ___________________________ figure, not a _________________________ one.

Commented [LN1]: To understand dilations with the origin as the center of dilation.

Commented [LN2]: Dilation

Commented [LN3]: Increases

Commented [LN4]: decreases

Commented [LN5]: Scale Factor

Commented [LN6]: dilation

Commented [LN7]: similar

Commented [LN8]: proportional

Commented [LN9]: remain the same

Commented [LN10]: similar

Commented [LN11]: congruent

BRONZE 1. Graph the dilated image of triangle XYZ using a scale factor of 2 and (0,0) as the center of dilation.

What is the rule for this dilation?

2. Triangle ABC is dilated to create its image, triangle A’B’C’.

What is the scale factor for this dilation? ______ What is the rule? _____________________________________

B

Commented [LN12]: Look back at last class notes. What was our rule for dilation? How do we properly represent this?

Commented [LN13]: Make a table or chart for you to write down the points. Label them ABC and A’B’C’. Notice a pattern?? Good math habits make for an efficient student!

3. Graph the dilated image of triangle XYZ, using a scale factor of 0.5 and (0,0) as the center of dilation. X: _____ X’:_____ Y: _____ Y’: _____ Z: _____ Z’: _____

4. Graph the dilated image of quadrilateral MNOP using a scale factor of 1.5 and the origin as the center of

dilation.

5. In the diagram above, what are the coordinates for quadrilateral M’N’O’P’?

a. M’ (-6, 3) N’ (3, 3) O’ (6, -3) P’ (-4, -4) b. M’ (-6, 3) N’ (3, 3) O’ (-6, -6) P’ (6, -3) c. M’ (-6, -6) N’ (6, -3) O’ (3, 3) P’ (-6, 3) d. M’ (-6, 3) N’ (3, 3) O’ (6, -3) P’ (-6, -6)

Commented [LN14]: Could we use the fraction form of a decimal? Sure. Whatever makes you comfortable and efficient.

6.

7.

8. The width of a picture is 20 cm. Using a copy machine, you reduce the width of the picture to 5 cm. What is the scale factor of the dilation?

A 5

B 4

C 1

4

D 1

5

9. Consider triangle XYZ. For which of these transformations will the measure of the angles change?

A dilation

B reflection over the x-axis

C rotation 90˚

D none of the above

10. Alan dilates quadrilateral GHIJ by a scale factor of 4. The coordinate pair for J is (b, q). What are the coordinates for J’?

A (4b, q)

B (b, 4q)

C (b, q/4)

D (4b, 4q)

11. Given the coordinates for each set of vertices, choose the appropriate transformation.

A Dilation with a scale factor of 2

B Dilation with a scale factor of 0.5

C Translation 4 units left, 2 units down

D Translation 2 units right

12. Given the coordinates for each set of vertices, choose the appropriate transformation.

a. Dilation with a scale factor of 2 b. Dilation with a scale factor of 0.5 c. Translation 2 units left, 4 units up d. Translation 2 units right, 4 units up

13. All of the following results in an image that is congruent to the figure except:

A Rotation

B Dilation

C Reflection

D Translation

Triangle QRS Triangle Q’R’S’

Q: (8, 4) Q’: (4, 2)

R: (-6, -2) R’: (-3, -1)

S: (-4, 0) S’: (-2, 0)

Commented [LN15]: How do you check if this is a dilation or a translation? Write a rule for this transformation. (x, y) ______

SILVER 14. The chart below shows the coordinates for the vertices of rectangle ABCD. Rectangle ABCD undergoes a dilation of a scale factor of 0.25, resulting in rectangle A’B’C’D’. What are the coordinates of the new rectangle?

Rectangle ABCD Rectangle A’B’C’D’

A: (0, 2)

B: (2, 8)

C: (4, 8)

D: (0, 4)

15. The chart below shows the coordinates for the vertices of quadrilateral DEFG. Quadrilateral DEFG

undergoes a dilation of a scale factor of 1

3 , resulting in quadrilateral D’E’F’G. What are the coordinates of the

new quadrilateral?

Quadrilateral DEFG Quadrilateral D’E’F’G

D: (3, -6)

D’:

E:

E’: (3, 12)

F: (-1, 2)

F’:

G:

G’: (-6, 9)

GOLD

16. Graph the dilated image of line segment AB using a scale factor of 1

3 and the origin as the center of dilation.

Explain how you determined point B’: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ How many times as long is the new segment A’B’ compared to segment AB? __________________________________________________________________________________________ What do you notice about the two line segments? __________________________________________________________________________________________

THE ANSWERS continued 6. C 7. C 8. C 9. D 10. D 11. B 12. C 13. B 14.

Rectangle ABCD Rectangle A’B’C’D’

A: (0, 2) (0, 0.5) OR (0, ½)

B: (2, 8) (0.5, 2) OR ( ½, 2)

C: (4, 8) (1, 2)

D: (0, 4) (0, 1)

15.

Quadrilateral DEFG Quadrilateral D’E’F’G

D: (3, -6) D’: (1, -2)

E: (9, 36) E’: (3, 12)

F: (-1, 2) F’: (−1

3,2

3)

G: (-18, 27) G’: (-6, 9)

16.

A’B’ is one-third as long as AB. A’B’ and AB are parallel.

B’ A’