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Holliday’s 8th Grade Math Week 9 May 11-15We are going to continue looking back at previous lessons and do some review of skills that will help us next year in 9th grade. Since we have already completed the independent practice for these lessons we will continue to do the online homework assignments. Please either do the online version or the paper version that can be found in the pdf. In all you will have 4 online homework assignments and one Galileo Quiz.

Monday May 11

Online WorkLesson 9.3 Properties of Rotations (8.G.1, 8.G.3)

Objective: Students will verify experimentally the properties of rotations, reflections, and translations and describe the effect of dilations, translations, rotations, and reflections, on two dimensional figures using coordinates.

If you need a refresher on lesson 9.3 you can go to interactive student edition (above my assignments), Transformational Geometry Module 9 and lesson 9.3. This will open in a new window for the lesson. Please complete the 9.3 Homework in your “My Assignments” section. Any questions please email and I will gladly assist in due time.

Email me at: [email protected]

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Packet VersionThe 9.3 review lesson can be found on Pgs. 291-296 in your go math books. If you are unable to do the online math please use the lesson 9.3 Homework consumable (see downloadable PDF) and either print and finish or write the problem and answer on another sheet of paper. Once completed please scan or take a picture and email to me with your name and lesson number.

Tuesday May 12

Online WorkLesson 9.4 Algebraic Representations of Transformations (8.G.3)

Objective: Students will describe the effect of dilations, translations, rotations, and reflections, on two dimensional figures using coordinates.



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Wednesday May13

Online WorkLesson 9.5 Congruent Figures (8.G.2)

Objective: Students will understand that a two dimensional figure is congruent to another is the second can be obtained from the first by a sequence of rotations, reflection, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.



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Thursday May 14

Online WorkLesson 10.1 Properties of Dilations (8.G.3, 8.G.4)

Objective: Students will understand that at two dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. Students will describe the effects of dilations, translations, rotations, and reflections on two dimensional figures using coordinates.

If you need a refresher on lesson 10.1 you can go to interactive student edition (above my assignments), Transformations and Similarity Module 10 and lesson 10.1. This will open in a new window for the lesson. Please complete the 10.1 Homework in your “My Assignments” section. Any questions please email and I will gladly assist in due time.


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Friday May 15

Galileo Quiz Week 9

Please Finish any work that was not completed on time and submit. Have a good weekend!

Lesson 9.3 - Homework Name________________________________

Question 1. A rotation in the coordinate plane is a transformation that turns a figure around a given (select) called the center of rotation.

Question 2. Siobhan rotates a right triangle 90° counterclockwise about the origin. Is the image of the triangle congruent to the preimage?

(select) , the figures (select) congruent.Question 3. Draw the image of the figure after a rotation of 180° about the origin.

Question 4. What are the properties of rotations? Complete the answer.

Rotations preserve (select) but change (select) .Question 5. The figure shows triangle ABC and a rotation of the triangle about the origin. How would you describe the rotation?

ABC was rotated ° counterclockwise. What are the coordinates of the image?

The coordinates are A′( , ), B′( , ), and

C′( , ).

Question 6. What type of rotation will preserve the orientation of the H-shaped figure in the grid?

A ° rotation will preserve the orientation of the figure.

Question 7. Complete the table with rotations of 180° or less. Include the direction of rotation for rotations of less than 180°.

Shape in quadrant Image in quadrant Rotation

I IV °

III I 180°

IV III90°

clockwise

Question 8. Complete the table with rotations of 180° or less. Include the direction of rotation for rotations of less than 180°.

Shape in quadrant Image in quadrant Rotation

I IV90°

clockwise

III I 180°

IV III °

(select)

Question 9. Draw the image of the figure after the given rotation about the origin. 270° counterclockwise

Question 10. Lucas is playing a game where he has to rotate a figure for it to fit in an open space. Every time he clicks a button, the figure rotates 90 degrees clockwise. What is the minimum number of times he needs to click the button so that each figure returns to its original orientation? Drag and drop each number into the correct box to complete the statements below.

He needs to click the button a minimum of time(s) for Figure A to return to its original orientation.He needs to click the button a minimum of time(s) for Figure B to return to its original orientation.He needs to click the button a minimum of time(s) for Figure C to return to its original orientation.Question 11. Point A is on the y-axis. Describe all possible locations of image A′ for rotations of 90°, 180°, and 270°. Include the origin as a possible location for A. Complete the answer.

If A is at the origin, A′ for any rotation about the origin (select) at the origin. Otherwise,

A′ is on the x-axis for ° and 270° rotations and on the y-axis for a ° rotation.

Lesson 9.4 - Homework Name___________________________________

Question 1. Triangle XYZ has vertices X(−6, 2), Y(−4, 4), and Z(−2, −2). Part 1Find the vertices of triangle X′Y′Z′ after a translation of 6 units to the right. The vertices are

X′( , ), Y′( , ), and Z′( , ). Part 2Graph triangle XYZ.

Part 3Graph the triangle's image.

Question 2. Use the rule (x, y) (y, −x) to graph the image of the triangle below. Then complete the description of the transformation.

The triangle is rotated ° clockwise.

Question 3. How do the x− and y−coordinates change when a figure is translated right a units and down b units?

Complete the answer. The x−coordinates (select) by a, and the y−coordinates (select)

by b.

Question 4. Part 1Enter an algebraic rule to describe the transformation.

(x, y) (x − , y − ) Part 2Complete the description of the transformation.

The translation is unit(s) to the left and unit(s) down.Question 5. Triangle XYZ has vertices X(8, −2.3), Y(6.5, 6), and Z(7, 5). When translated, X′ has coordinates (6.8, −0.3). Enter a rule to describe this transformation. Then find the coordinates of Y′ and Z′. Drag and drop each number into the correct box to complete the statements.

The rule is (x, y) x − , y + . The coordinates are Y′ , and Z′ , . 8 ,2,5.8, 1.2, 5.3, 7Question 6.Use the rule (x, y) (x − 2, y − 4) to graph image of the rectangle. Then complete the description of the transformation.

The rectangle is translated unit(s) to the left and unit(s) down.Question 7. Alexandra drew the logo shown on half-inch graph paper. Enter a rule that describes the translation Alexandra used to create the shadow on the letter A.

(x, y) Question 8.

Part 1Graph the triangle with vertices A (−3, 4), B (1, 5), and C (−4, −4) in blue. Then use the transformation (y, x) to graph its image in red.

Part 2

Which vertex of the image has the same coordinates as a vertex of the original figure? Give your answer and complete the explanation.

The vertex ( , ) has the same coordinates as the original figure. The x and y values are (select) , so switching x and y has no effect on the coordinates.

Part 3 Enter the equation of a line through the origin and this point. y = Complete the description of the transformation of the triangle. The triangle is reflected across the line y = .Question 9. Triangle ABC with vertices A(−4, −1), B(2, −1), and C(5, 5) is translated by (x, y) (x − 5, y + 8). Then the image, triangle A′B′C′, is translated by (x, y) (x + 6, y − 5), resulting in A″B″C″.Find the coordinates for the vertices of triangle A″B″C″.

The coordinates are A″( , ), B″( , ), and

C″( , ).

Enter a rule for one translation that maps triangle ABC to triangle A″B″C″. A single rule that

maps triangle ABC to triangle A″B″C″ is (x, y) (x + , y + ).

Lesson 9.5 - Homework Name ______________________________

Question 1. Apply the indicated series of transformations to the rectangle. Each transformation is applied to the image of the previous transformation, not the original figure. Each image is labeled with the letter of the transformation applied.

Part 1 A: Reflection across the y−axis

Part 2 B: Rotation 90° clockwise around the origin

Part 3 C: (x, y) (x − 2, y)

Part 4 D: Rotation 90° counterclockwise around the origin

Part 5 E: (x, y) (x − 7, y − 4)

Question 2. Identify a sequence of transformations that will transform figure B into figure C. What transformation is used to transform figure B into figure C?

A translation unit(s) right and unit(s) down is used to transform figure B into figure C.

Question 3. What does it mean for two figures to be congruent? Complete to form the best answer.

The figures have the (select) .

Question 4. After a sequence of translations, reflections, and rotations, what is true about the first figure and the final figure? Complete the answer.

They have the (select) . (They (select) congruent.)

Question 5. For the given figure A, graph figures B and C using the given sequence of transformations. Select whether figures A and C have the same or different orientation.Part 1 Figure B: a translation of 2 units to the right and 4 units up

Part 2Figure C: a 90° clockwise rotation around the origin

Part 3

Figures A and C have (select) .Question 6. For the given figure A, graph figures B and C using the given sequence of transformations. Select whether figures A and C have the same or different orientation. Part 1 Figure B: a reflection across the y−axis

-

Part 2 Figure C: a translation 2 units down

Part 3

Figures A and C have (select) .Question 7. A city planner wanted to place the new town library at site A. The mayor thought that it would be better at site B. What transformations were applied to the building at site A to relocate the building to site B? Did the mayor change the size or orientation of the library?

The building at site A was translated unit(s) right and unit(s) down, then it was

reflected across the (select) −axis. The size (select) changed. The orientation (select) changed.

Question 8. The Commutative Properties for Addition and Multiplication state that the order of two numbers being added or multiplied does not change the sum or product. Part 1

Are translations and rotations commutative? Translations and rotations (select) commutative. Part 2If not, complete the counterexample. The point (4, 5), translated 3 units to the right, becomes

( , ), then rotated 90° clockwise around the origin it becomes

( , ). The point (4, 5) rotated 90° clockwise around the origin becomes (

, ), then translated 3 units to the right it becomes ( , ), which is not the same.Question 9. For the representation, describe a possible sequence of transformations. (x, y) (−x − 2, y + 1) Complete the description.

The representation is a translation unit(s) right and unit(s) up and a reflection cross

the (select) -axis.

Lesson 10.1 - Homework Name _______________________________

Question 1. Use triangles ABC and A′B′C′ shown below. For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates.

The ratio of the x-coordinates is .The ratio of the y-coordinates is .

Question 2. Use triangles ABC and A′B′C′ shown below. Find the ratios of the lengths of the corresponding sides of triangle A′B′C′ and triangle ABC.

The ratio of the lengths of the corresponding sides of triangle A′B′C′ and triangle ABC is .

Question 3. Use triangles ABC and A′B′C′ shown below. Find the scale factor of the dilation.

The scale factor of the dilation is .

Question 4. How can you find the scale factor of a dilation?

You can divide a side length of the (select) by the corresponding side length of the (select) to calculate the scale factor of a dilation.

Question 5. Tell whether one figure is a dilation of the other or not. Complete the explanation of your reasoning. Quadrilateral MNPQ has side lengths of 30 mm, 42 mm, 54 mm, and 51 mm. Quadrilateral M′N′P′Q′ has side lengths of 5 mm, 7 mm, 9 mm, and 6 mm. The figure M′N′P′Q′

(select) a dilation of the figure MNPQ. The ratios of the lengths of the corresponding sides (select) equal.

Question 6. Tell whether one figure could be a dilation of the other or not. Complete the explanation of your

reasoning. Two triangles, Triangle 1 and Triangle 2, are similar. Triangle 1 (select) a dilation of (select)

Triangle 2. The ratios of the lengths of the corresponding sides equal.Question 7. Tell whether one figure is a dilation of the other or not. Complete the explanation of your reasoning.On a coordinate plane, triangle UVW has coordinates U(20, −12), V(8, 6), and W(−24, −4). Triangle U′V′W′ has

coordinates U′(5, −3), V′(2, 1.5), and W′(−6, −1). The figure U′V′W′ (select) a dilation of the figure

UVW. The ratios of the lengths of the corresponding sides (select) equal.Question 8. Write "same" or "changed" into the correct boxes to compare the image of a reflection with the original figure.

Image Compared to Original Figure

Orientation Size Shape

Reflection

Question 9. Write "same" or "changed" into the correct boxes to compare the image of a dilation with the original figure.

Image Compared to Original Figure

Orientation Size Shape

Dilation

Question 10.

Identify the scale factor used in the dilation. The scale factor is .

Question 11. Complete the explanation of how you can find the center of dilation of a triangle and its dilation.

Locate the corresponding (select) of the triangles and draw lines connecting each pair of (select) . The lines will (select) at the center of dilation.

Question 12.Part 1 A square on the coordinate plane has vertices at (−3, 3), (3, 3), (3, −3), and (−3, −3). A dilation of the square has vertices at (−6, 6), (6, 6), (6, −6), and (−6, −6). Find the scale factor and the perimeter of each square.

The scale factor is . The perimeter of the original square is and the perimeter of the image

is .Part 2A square on the coordinate plane has vertices at (−4, 4), (4, 4), (4, −4), and (−4, −4). A dilation of the square has vertices at (−8, 8), (8, 8), (8, −8), and (−8, −8). Find the scale factor and the perimeter of each square.

The scale factor is . The perimeter of the original square is and the perimeter of the image

is .

Part 3Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image.

The perimeter of the image is the perimeter of the original figure (select) (select) .

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