Name: ______________________________________ Class: ______________ Date: ____________

Unit 5: Butterflies, Pinwheels, & Wallpaper

Directions: Please complete the necessary problems to earn a maximum of 10 points according to the

chart below. Show all of your work clearly and neatly for credit- which will be earned based on

completion rather than correctness.

I can complete transformations of shapes on a coordinate plane.

Lesson Practice problems Options Maximum

Points

Lesson 1: Flipping on a Grid

1, 2, 3, 8

3 Points

Lesson 2: Sliding on a Grid

4, 5, 9 2 Points

Lesson 3: Spinning on a Grid

6, 7, 10 2 Points

Lesson 5: Parallel Lines, Transversals, and Angle Sums

11, 12, 13, 14 3 Points

______/ 10 Points

Name: ______________________________________ Class: ______________ Date: ____________

For Exercises 1 – 7, use the figure below and find the image of the figure after each transformation.

1. Complete the table showing the coordinates of points A – E and their images after a reflection in the y – axis.

Point A B C D E Original Coordinates (-5, 1) (-2, 5) (0, 2) (-2, 3) (-3, 0)

Coordinates After a y-axis Reflection (5, 1) (2, 5) Coordinates After a x-axis Reflection (-5, -1) (-2, -5) (-2, -3)

Coordinates After a x-axis Reflection Followed By a y-axis Reflection

(2, -5) (0, -2) (2, -3)

a. Draw the Image.

b. Write a rule relating coordinates of key points and their images after a reflection in the

y-axis: (x, y) ( ____ , ____ ).

2. Add a row to your table for Exercise 1 to show the coordinates of points A – E and their images after a reflection in the x- axis.

a. Draw the image. b. Write a rule relating coordinates of key points and their images after a reflection in the

x-axis: (x, y) ( ____ , ____ ).

3. Add another row to your table from Exercise 1 to show the coordinates of points A – E and their images after a reflection in the x-axis, followed by a reflection in the y-axis.

a. Draw the image. b. Write a rule relating coordinates of key points and their images after bother reflections:

(x, y) ( ____ , ____ ). c. Multiple Choice. What single transformation in this Investigation has the same effect as

the sequence of two line reflections? i. half- turn rotations

ii. 1 unit to right, down 5 units translation iii.

Name: ______________________________________ Class: ______________ Date: ____________

4. Complete the table showing the coordinates of points A – E and their images after a translation

that “moves” point B to point (3, 4).

Point A B C D E Original Coordinates (-5, 1) (-2, 5) (0, 2) (-2, 3) (-3, 0)

Coordinates After Translating B to (3, 4) (0, 0) (5,1) (2, -1) Coordinates After Translating B’’ to (-1, 0) (-4, -4) (-1, 0) (1, -3)

a. Draw the image. b. Write a rule relating coordinates of key points and their images after the translation: (x,

y) ( ____ , ____ ).

5. Add a row to your table from Exercise 4 to show the coordinates of points A – E and their images after the first translation, followed by a translation that “moves” points B’ to (-1, 0).

a. Draw the image. b. Write a rule relating coordinates of key points and their images after the second

translation: (x, y) ( ____ , ____ ). c. Write a rule relating coordinates of key points and their images after the sequence of

the two translations: (x, y) ( ____ , ____ ). d. Multiple Choice. What single information is equivalent to the sequence of the two

translations? i. half- turn rotations

ii. 1 unit to right, down 5 units translation iii.

Name: ______________________________________ Class: ______________ Date: ____________

6. Complete the table showing the coordinates of points A – E and their images after a counterclockwise rotation of 90° about the origin.

Point A B C D E Original Coordinates (-5, 1) (-2, 5) (0,2) (-2, 3) (-3, 0)

Coordinates After a 90° Rotation (-1, -5) (-2, 0) (-3, -2)

Coordinates After a 180° Rotation (5, -1) (0, -2) (3, 0)

a. Draw the image. b. Write a rule relating coordinates of key points and their images after a rotation of 90°:

( x, y) ( ____ , ____ ).

7. Add a row to your table from Exercise 6 to show the coordinates of points A – E and their images after two counterclockwise rotations of 90° about the origin.

a. Draw the image. b. Write a rule relating coordinates of key points and their images after both rotations:

(x, y) ( ____ , ____ ). c. Multiple Choice. What single transformation is equivalent to the sequence of the two

rotations? i. half- turn rotations

ii. 1 unit to right, down 5 units translation

8.

Name: ______________________________________ Class: ______________ Date: ____________

Complete the table showing the coordinates of points A – C and their images after a reflection in the line

y = x.

Point A B C Original Coordinates (0, 2) (1, 5) (3, 5)

Coordinates After a Reflection in y = x (5, 1) Coordinates After a Reflection of Triangle A’B’C’ (2, 0) (5, -3)

b. Draw the image and label the vertices A’, B’, and C’.

c. Add a row to your table to show the coordinates of points A – C and their images after a

reflection of triangle A’B’C’ in the axis.

d. Draw the image and label the vertices A”, B”, and C”.

e. Draw the image of triangle ABC after the same two reflection, but in the reverse order.

That is, reflect triangle ABC in the x-axis and then reflect its image, triangle A’B’C’ in the

line y = x. What does the result suggest about the commutativity of a sequence of line

reflections?

9.

i. Translate ABC according to the rule (x, y) (x + 2, y – 3). Label its image A’B’C’.

ii. Translate ABC according to the rule (x, y) (x – 4, y – 6). Label its image A”B”C”.

Name: ______________________________________ Class: ______________ Date: ____________

b. Use the coordinates of the vertices of triangle ABC and its two images to compare the

slopes of each pair of line segments.

The slopes of AB and A’B’ are both ____.

The slopes of AC and A’C’ are both ____.

The slopes of CB and C’B’ are both _____.

The slopes of AB and A”B” are both ____.

The slopes of AC and A”C” are both ____.

The slopes of CB and C”B” are both _____.

c. Multiple Choice. What do your results from parts (a) and (b) say about the effect of

translations on the slopes of lines? About the relationship between a line and its image

under a translation?

i. Translations ignore the slope of lines and does not map lines onto parallel lines.

ii. Translations preserve slopes of lines and maps lines onto parallel lines.

10. a. Use triangle ABC from Exercise 8. Draw triangle ABC on a coordinate grid and its image

after a 180° rotation about the origin. Label the Image A’B’C’.

b. Use the coordinates of the vertices of triangle ABC and its image to compare the slopes

of each pair of line segments.

Slopes of both AB and A’B’ are both _____.

Slopes of both AC and A’C’ are both _____.

Name: ______________________________________ Class: ______________ Date: ____________

Slopes of both CB and C’B’ are both ______ .

c. What do your results from part (a) and (b) say about the effect of half-turns or 180°

rotations on the slopes of line? About the relationship between a line and its image

under a 180°

11. In the diagram below, line L1 and L2 are parallel. What are the measures of angles a – g?

*** remember opposite angles equal the same measurement, adjacent angles add up to 180°.

Angles a, c, and e all measure ______.

Angles b, d, f, and g all measure _____.

12. What are the measures of angles a and b in the triangle?

*** remember adjacent angles add up to 180°.

13. What is the value of x in the diagram?

** remember angles in a Triangle add up to 180°.

Name: ______________________________________ Class: ______________ Date: ____________

14. The diagram shows parallelogram ABCD with one diagonal DB. Assuming only that opposite

sides of any parallelogram are parallel:

a. Which angles are congruent? How do you know?

b. How can you be sure that triangle ABD is congruent to triangle ADB? What are the

corresponding vertices, sides, and angles?

c. How does the congruence of triangles ABD and ADB guarantee that, in a parallelogram,

opposite sides are the same length?

Exit Ticket Level of Understanding

After finishing this investigation you should be comfortable doing the following: -using coordinate methods to study flips, turns, and slides. -understanding the properties of parallel lines. -understanding the properties of angles in triangles