lesson 10 2 algebraic representations of dilations

Mike DeVor. c. (x, y) (x, 2y) A: (x, y) (-x, y) b. _____________, Answer: b. Type below: The figure is reflected across the x-axis and dilated by a scale factor of 3. 5/2 = 2.5 HMH Into Math Grade 8 Module 2 Lesson 2 Answer Key Explore Dilations. Displaying all worksheets related to - Algebraic Representations Of Dialations. The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals _______. A dilation can produce a larger figure or an enlargement or a smaller figure or a reduction. Students can overcome their difficulties with the help of the Go Math Grade 8 Chapter 10 Transformations and Similarity Answer Key. Critical Thinking MNOP has vertices at M'(3, 4), N'(6, 4), O'(6, 7), and P'(3, 7). How many feet? This is a bundle of all first grade Illustrative Math-Friendly Units 1-8. C (7.5, 6) Perform a dilation on the coordinate plane. 21.1 Parallel Lines Cut by a Transversal. Original perimeter: 16 Type below: ratio of y-coordinates = 2/1 = 2 Describe the transformations that will transform the image back into the original figure. How can you use dilations to solve real-world problems? _____________. figure C Answer: Answer: Justify your answer. The vertices of the dilated image are A'(1, 1), B'(3, 1), and C'(1, 3). In the given expression, we can notice that the x coordinate is multiplied with 0.5 and that the y-coordinate is multiplied with 1.5. MN = $\sqrt{9}$ PPT - Algebraic Representations of Dilations PowerPoint Presentation Write the coordinates of the vertices of the preimage in the first column of the table. Classify each as such and justify your reasoning. Critical Thinking MNOP has vertices at M(3, 4), N(6, 4), O(6, 7), and P(3, 7). _____________, Answer: The stage crewmembers calculation is incorrect. a dilation produces an image similar to the original figure, Question 10. The square is dilated under the dilation (x, y) (0.25x, 0.25y). coordinates for B (x, y) -> (2.5x, 2.5y), Question 3. (0, 1) a. a = -3 Multistep As with geometric figures, graphs can be transformed through translations, reflections, rotations, and dilations. ALGEBRAIC REPRESENTATIONS OF DILATIONS When a dilation in the coordinate plane has the origin as the center of dilation, we can find points on the dilated image by multiplying the x and y coordinates of the original figure by the scale factor. At least one transformation must be a dilation with a scale factor other than 1, Question 6. Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? Question 9. A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. k = $\frac{2}{3}$, Next, Let us represent the dilation algebraically, using A'(-15, -12), B'(6, 12) and C'(12, -9). C. Apply the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. Answer: Type below: (x, y) (0.8x, 0.8y) d. What are the perimeter and area of the image? A stage crewmember writes (x, y) ($\frac{1}{12}$x, $\frac{1}{12}$y) to represent the dilation. On a coordinate plane, triangle UVW has coordinates U(20, 12), V(8, 6), and W(24, -4). F (3, 3) scale factor of 1.5 lesson 10 2 algebraic representations of dilationsmercedes financial services phone numbermercedes financial services phone number b. 6cm 40 = 240cm A = (-4, 4), A = (-2, 2); The triangles have only one pair of congruent angles, Question 2. When k is between 0 and 1, the dilation is a reduction by the scale factor k. G(5, 2) G'(5 1.5, 2 1.5) G'(7.5, 3) (2) Explain. Apply each transformation to the image of the previous transformation. Original perimeter: _________ Question 16. d. y = 3x 1, Explanation: Question 2. lesson 10 2 algebraic representations of dilations; Type below: A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). A: (x, y) (-x, y) 320, Algebraic Representations of Dilations Page No. Original perimeter: 16 _____________, Explanation: The center of dilation is the origin and (x, y) (3x, 3y). If you want to learn the best way of solving maths, students can immediately start their practice with the help of the Go Math Grade 8 Chapter 10 Transformations and Similarity Answer Key. Page 333: Ready to Go On? Explain your reasoning. PDF LESSON Algebraic Representations of Dilations 13-2 Practice and Problem The backdrop scale factor is 1/20, not 1/12, Question 12. Then apply the dilation (x, y) ($\frac{3}{2}$x, $\frac{3}{2}$y) and write the coordinates of the vertices of the image in the second column. Perimeter = ________ units (0, 4) Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. 325. . MNPQ is not a dilation of MNPQ, Explanation: F (3, 3) (x, y) (x, 2y) Grade 8 HMH Go Math - Answer Keys Answer keys Chapter 10 Question 9. _____________, Answer: (x, y) -> (x, -y); (x, y) -> (3x, 3y), Question 4. Worksheets are Middle school math series course 2, Chapter 7, Algebraic representations of dilations, Algebraic representations of dilations, Conjectures. A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) _____________, Answer: Dilation is defined as a transformation that changes the size of a figure. Explanation: Question 5. 0 = -2x + 6 A: (x, y) (-x, y) Save. A dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction). d. A rectangular room has coordinates Q(2, 2), 6(7, 2), S(7, 5), and T(2, 5) on the blueprint. _____________, Explanation: View this Page Math 7 Accelerated - Computech Mathematics https://darthmuster.com/math-7-accelerated/ Transformation and Similarity, 20.1 Properties of Dilations 20.2 Algebraic Representations of Dilations 20.3 Similar Figures. (-6, -2) N-gen Math 7 Unit 6 Answer Key AB/AB = 2/4 = 1/2 velvet carpet for bedroom. The angle measures are the same After dilation Find the lengths of the sides of the actual sign. perimeter of the original square = 4 + 4 + 4 + 4 = 16 (7, 8) 24/8 = 3 mm One inch on the blueprint represents 1 48 feet = 48 $\frac{1}{12}$ inch = 4 inch, c. Write the algebraic representation of the dilation from the blueprint to the house. b. _____________, Explanation: Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. (0, 4) (-7, -8) scale factor = 1/2, Question 19. Question 5. (x, y) -> (2x, 2y), Question 9. (x, y) -> (1/4x, 1/4y) (x, y) ($\frac{3}{2}$x, $\frac{3}{2}$y) Algebraic Representations of Dilations - 2. Clifford Algebras - Daniel Klawitter 2014-10-29 After revising known representations of the group of Euclidean displacements (1, -1). Find the scale factor and the perimeter of each square. Algebraic Representations of Dilations Success for English Learners A dilation changes the size of a figure without changing its shape. _____________, Explanation: 10-2. lesson. (-2, 1) 77% average accuracy. Type below: (-4, -2) (Explore Activities 1 and 2) _____________, Answer: If you found any of these problems to be difficult, select the times table you are struggling with from the list of Related Lessons in the right-hand sidebar, and go back to review those multiples before moving forward. 10.2 Algebraic Representation of Dilation - YouTube (-2, -2), Question 12. endstream endobj 135 0 obj <>stream Then apply the dilation (x, y) ($\frac{3}{2}$x, $\frac{3}{2}$y) and write the coordinates of the vertices of the image in the second column. algebraic rule: (x, y) -> (1/3x, 1/3y), Question 4. Lets find the ratio oft: x-coordinates of corresponding points Time Squared Activity: Each participant gets 3 pages with 24 squares representing the hours in a day. What are the coordinates? Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Rectangle FGHI(x, y) (1.5x, 1.5y) Question 3. Write the algebraic representation of the dilation shown. b. But before this, let us soLve first the length of one side of the dilated image and the corresponding length of the originaL image using the distance formula d. The shorter leg of the drawing is currently on the left. Then write them algebraically. If the dilation produce a larger figure the line segments of the dilated figure is longer than the original figure Also, if the dilation produce a smaller figure, the line segments of the dilated figure is smaller than the original figure. height: |QT| = |6.25 2.5| = 3.75 inch a = 5, Question 5. No; the dilation is not the same reversed, Explanation: x = 3 2), (3.6)) -> B'(6, 18) _____________, Answer: (-2, -2) a = 15/3 area = l.w = 2 . Translate the image 3 units down and 6 units right and dilate it by a factor of 2 I (3, 6) 37, 53, and 90, Question 6. c. Write the algebraic representation of the dilation from the blueprint to the house. (1, 1) (Example 1). No; one figure is not a dilation of the other, Explanation: Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. figure C Options: 21.1 Parallel Lines Cut by a Transversal. _____________. _____________, Answer: ratio of y-coordinates = 2, Explanation: For 711, tell whether one figure is a dilation of the other or not. _____________, Answer: How many feet? Two triangles, Triangle 1 and Triangle 2, are similar. 10.2 Algebraic Representations of Dilations. The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals 2. How does multiplying a constant by the x variable of a function affect its graphical representation? During the video lesson have students: Take notes on the material. (x, y) -> (1.5x, 1.5y) Algebraic Representations Of Dilations - Lesson Worksheets Thus, the dilation has no effects on the measures of the angles of the image. In this lesson, you will learn multiples of 11. _____________, Answer: The coordinates of the vertices of the original image are multiplied by $\frac{1}{2}$ for the purple square. a. a dilation by a scale factor of 4 Options: _____________, Explanation: Quadrilateral DEFG has sides measuring 16 m, 28 m, 24 m, and 20 m. Quadrilateral DEFG has sides measuring 20 m, 35 m, 30 m, and 25 m. Type below: The business owner wants it to remain on the left after the hypotenuse goes to the top. The students of 8th standard can easily learn maths with the Go Math Solution Key on ccssmathanswers.com, Lesson 2: Algebraic Representations of Dilations, Question 1. Describe the transformations that will transform the image back into the original figure. The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals _______. Type below: lesson 10 2 algebraic representations of dilations Apply the indicated sequence of transformations to the square. e. What are the dimensions of the new room, in inches, on the blueprint? Type below: _____________. A: (x, y) (-x, y) _____________. Algebraic Representations of Dilations. 324, Algebraic Representations of Dilations Page No. _____________, Answer: ratio of x-coordinates = -4/-2 = 2 Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. PDF Algebraic Representations of Dilations HW - nobelms.com Graph the image of the figure using the transformation given. c. Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image. The blue square is the preimage. The lengths are 240 cm, 320 cm, and 400 cm, Question 6. (x, y) (0.8x, 0.8y) y = -1/3 . What is the algebraic representation of this dilation? _____________, Answer: (x, y) -> (2x, 2y), Question 9. ________. a. The figure is reflected across the y-axis and dilated by a scale factor of 4. Type below: The scale factor of the dilation is 2. What is the algebraic representation of this dilation? (x, y) -> (x, y+6) _____________, Answer: Type below: R'(8.75, 2.5), a year ago. (x, y) (x, 2y) (2, 2) Describe two transformations that will do this. House dimensions: 25ft by 15ft, Question 10. Scale factor = 2 Filled table is shown in the picture below. algebraic rule: (x, y) -> (1.5x, 1.5y), Question 3. After calculating the coordinates, we can graph every point of the image after dilation and connect them to get the wanted figure. (-1, -1) Answer: x + 1 Answer: lesson 10 2 algebraic representations of dilations After dilation A(0, 8), B(0, 0), C(10, 0) 3. Rotate the drawing 180 around the origin. MN = 3, Now, let us determine the value of k, that is (2, -2) ________ inches A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). ________ feet, Question 9. So, the corresponding S are congruent. _____________, Answer: x = 3 B: Rotate the square 180 around the origin. 15/5 = 3 mm (9, 6), (3, 6), (9, 3), (3, 3) b. Coordinates after dilation A(8, 0) A' . How can you find the scale factor of a dilation? perimeter of the original square = 6 + 6 + 6 + 6 = 24 Sketch triangle ABC and ABC for the dilation (x, y) (-2x, -2y). So, the scale factor of the dilation is 3/4. (x, y) (0.5x, 1.5y) The arrow shown is the preimage. Mod 20-2 Class Problems. a. y = 2x + 6 The blueprints are plotted on a coordinate plane. This is called a reduction. Triangle XYZ has angles measuring 29 and 92. figure B y = 3x 1 The vertices of the dilated image are F'(3.5, 3.5), G'(7.5, 3.5), H'(7.5, 6) and I'(, 9). 130 0 obj <>stream In this unit we review the basic concept of a function and emphasize multiple representations of these foundational tools. D. Sketch the image after the dilation on the coordinate grid. Question 16. 332, Big Ideas Math Answers Grade 7 Accelerated, Bridges in Mathematics Grade 4 Home Connections Unit 5 Module 1 Answer Key, Bridges in Mathematics Grade 4 Home Connections Unit 5 Module 2 Answer Key, Bridges in Mathematics Grade 4 Home Connections Unit 5 Module 3 Answer Key, Bridges in Mathematics Grade 4 Home Connections Unit 5 Module 4 Answer Key, Bridges in Mathematics Grade 4 Home Connections Unit 3 Module 4 Answer Key, Bridges in Mathematics Grade 4 Home Connections Unit 3 Module 3 Answer Key, Bridges in Mathematics Grade 4 Home Connections Unit 3 Module 1 Answer Key, Bridges in Mathematics Grade 4 Home Connections Unit 3 Module 2 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 5 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 5 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 5 Module 2 Answer Key. G7 Math Lesson 10.2 Algebraic Representations of Dilations STUDY Flashcards Learn Write Spell Test PLAY Match Gravity algebraic expression Click card to see definition Click again to see term 1/15 Created by weiennlee TEACHER Terms in this set (15) algebraic expression dilation vertex (plural: vertices) (:vertices) MN = $\sqrt{(6-3)^{2}+(4-4)^{2}}$ Type below: Depending on the scale factor, dilation may increase or decrease the starting object. Properties of Dilations Lesson Check Page No. (x, y) -> (x+3, y+5), Question 5. c. y = $\frac{2}{3}$x 2 y = 2/3 . k = $\frac{3}{4.5}$ After dilation Sketch the image of the figure after the dilation. figure D Edit. (0, -4) By, definition of a dilation in which it can only be enlarged or reduced with respect to the scale factor k between 0 and 1 or greater than 1, respectively, if the scale factor in the dilation is equal to 1, then the image would be the same as the preimage. . ratio of x-coordinates = _______ A dilation of (x, y) (kx, ky) when 0 < k < 1 has what effect on the figure? The solution for this requires that you take the fifth root of both sides. Lets find the ratio of length $\frac{20}{400}$ = $\frac{1}{20}$ In feet 6.25 4 = 25ft and 3.75 4 = 15 ft, Question 10. Ilustrative Math Grade 3 Unit 8 Lesson 2 Teaching Resources | TPT x = 1/3, Question 6. _____________, Answer: b. coordinates for A 10.2 Practice B Answer Key - cismoore.org A (3, 3) B'((3. Name:&_____& &&&&&Date:&_____& Lesson:'10.2'Algebraic'Representations'of'Dilations'' The HMH Go Math 8th Grade Chapter 10 Transformations and Similarity Solution Key includes properties of dilations, Algebraic Representations of Dilations, and similar figures. If two figures are similar but not congruent, what do you know about the sequence of transformations used to create one from the other? a. y = 2x + 6 (-3, -8) Perimeter = ________ units 325, Algebraic Representations of Dilations Lesson Check Page No. Dilate each figure with the origin as the center of dilation. Triangle UVW has coordinates U(15, 9), V(6, 4.5), and W(18, -3). d = $\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$ _____________. Then write an algebraic rule to describe the dilation. I know that triangle ABC is a dilation of triangle ABC because the ratios of the corresponding x-coordinates are _______ and the ratios of the corresponding y-coordinates are _______. Notes. PDF Algebraic Representations of Dilations - nobelms.com (1, -1) b. _____________, Answer: Answer: (-2, 0) (x, y) -> (-x, y), Question 11. On a computer, Raquel uses polygons and a circle to make a model of the top of London's Big Ben clock . Type below: Type below: (3, 2), (1, 2), (3, 1), (1, 1) R'(8.75, 2.5), c. a = 5 Date Class LESSON Algebraic Representations of Dilations Reteach You dilate a figure using the origin as the center of . y = -2x + 6 How does the dilation affect the length of line segments? (x, y) -> (-x, y); (x, y) -> (x, 3y) Then write them algebraically. %PDF-1.6 % a. lesson 10 2 algebraic representations of dilations Algebraic Representation: Meaning & Examples | StudySmarter _____________, Question 12. $\frac{-\frac{1}{2}}{-2}=\frac{\frac{1}{2}}{2}=\frac{1}{4}$ Explain how this can happen. (9, 6), (3, 6), (9, 3), (3, 3), Question 2. A dilation of (x, y) (kx, ky) when 0 < k < 1 has what effect on the figure? B (7.5, 3) ADDITIONAL EXAMPLE 1 Graph the image of rectangle JKLM after a dilation with the origin as its center and a scale factor of 2. d. (x, y) ($\frac{2}{3}$x, y) MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). If the center of dilation is the origin and the scale factor is 3, graph the dilated image P'Q'R'. 715 Module 20 Lesson 2 Algebraic Representation of Dilation DRAFT. There must be an even number of dilations and for each dilation applied to the figure, a dilation that has the opposite effect must be applied as well. Type below: Write the algebraic representation of the dilation shown. What will the dimensions of the new room be, in feet, in the new house? ratio of x-coordinates = 4/2 = 2 x = 3 The grid shows a diamond-shaped preimage. (x, y) -> (x+3, y+5), Question 5. endstream endobj 134 0 obj <>stream Algebraic Representation Of Dialation - Lesson Worksheets Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? What is the effect of a negative scale factor? $JTdDP~~@ x PPT PowerPoint Presentation 0 = 2/3 . Area = 64 square units, Explanation: Miultiply each coordinate of the vertices of ABC by 3 to find the vertices of the dilated image. Worksheets are Lodwlrqv3udfwlfh, Do not edit changes must be made through file info, Correctionkeyb transformations and similarity module 10, Graph the image of the figure using the transformation, Pre algebra, Lesson algebraic representations of transformations 9 4, Translations of shapes, Trainerinstructor notes . _____________. ________ feet, Question 9. cfelg. The center of dilation is the origin. x 2 Question 3. class problems. Unit 9 Review. I can describe what happens when two-dimensional figures are transformed using coordinates. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. a. _____________, Question 9. _____________, Answer: lesson 10 2 algebraic representations of dilations ALGEBRAIC REPRESENTATIONS OF DILATIONS WORKSHEET Problem 1 : The triangle PQR shown on the grid is the pre-image. Given M(4.5, 6), N(9, 6), 0(9, 10.5), P(4.5, 10.5) and M'(3, 4), N'(6, 4), O'(6, 7), M(3, 7) center at the origin, Let us represent the dilation algebraically. _____________, Answer: _____________, Answer: Many students have loved the way of explanation given on Go Math Grade 8 Answer Key on our website. The business owner wants it to remain on the left after the hypotenuse goes to the top. C = (-2, -4), C = (-1, -2); The dimension of a new room on a blueprint is now: (-4, 0), Question 4. a year ago. Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). What is the algebraic representation of this dilation? The first one is done for you. a. The homeowner wants this room to be 25% larger. Scale factor: 2 146 practice pages that can be used as year-long:Cool-downs or homeworkUnit 1 - 14 lessonsUnit 2 - 22 lessons Unit 3 - 29 lessonsUnit 4 - 23 lessonsUnit 5 - 14 lessonsUnit 6 - 17 lessonsUnit 7 - 17 lessonsUnit 8 - 10 lessons38 AssessmentsUnit 1 . a. endstream endobj 136 0 obj <>stream The center of dilation is the origin and (x, y) (3x, 3y). (-6, 1), Question 13. (0, -6) Answer: Type below: (-6, -1) When 0 < k < the dilation is a reduction of the original by the scale k. What k > 1 the dilation is a enlargement of the original by the scale k. Explanation B: ratio of y-coordinates = _______ Echocardiography technique, (-4, 4) The figure is dilated by a scale factor of 5 and rotated 90 clockwise. c. The drawing has the hypotenuse on the bottom. BD/BD = 6/2 = 3 e. (x, y) (0.5x, 1.5y) 11,201. Scale factor: _________ Complete the table by writing same or changed to compare the image with the original figure in the given transformation. (-1, -1), Question 6. Type below: (9, 6), (3, 6), (9, 3), (3, 3), Question 2. -4/-2 =2; 4/2 = 2 (0, -4) dilation with a scale factor of 0.5 a = 15/3 Type below: (show solution) Question 6 (request help) Critical Thinking A triangle has vertices A (-5, -4), B (2, 6), and C (4, -3). Type below: 'LODWLRQV3UDFWLFH 6. (x, y) -> (1.5x, 1.5y) lesson 10 2 algebraic representations of dilationsbsn sports track order numberbsn sports track order number Which equation does not represent a line with an x-intercept of 3? horizontally shrinks by a factor of 2/3, Question 12. For enlargements, k > 1. b. Question 3. ratio of y-coordinates = -4/-2 = 2, Question 2. endstream endobj 133 0 obj <>stream scale factor of $\frac{1}{3}$ The division process is straightforward. Type below: The first idea is that we can construct representations of relationships between two sets of quantities and that these representations, which we call functions, have common traits. Quadrilateral MNPQ has side lengths of 5 mm, 8 mm, 7 mm, and 4 mm. Since the center of dilation is (0, 0), you can simply divide all . A. Triangle RST has angles measuring 38 and 75. _____________, Explanation: Type below: Green square: (x, y) (2x, 2y) The coordinates of the vertices of the original image are multiplied by _1 2 DRAFT. (x, y) (2.5x, 2.5y) _____________. perimeter of the original square = 4 + 4 + 4 + 4 = 16 If you draw a line connecting each pair of corresponding vertices, the lines will intersect at the center of dilation, Question 20. scale factor of $\frac{1}{3}$ What are the coordinates of the vertices of the image after a dilation with the origin as its center and a scale factor of 1.5? Explain. 8cm 40 = 320cm ratio of y-coordinates = _______ The blue square ABCD is the preimage. 320, Algebraic Representations of Dilations Page No. Therefore, MNPQ is not a dilation of MNPQ, Question 8. _____________, Answer: x + 1 The grid shows a diamond-shaped preimage. Type below: Critique Reasoning The set for a school play needs a replica of a historic building painted on a backdrop that is 20 feet long and 16 feet high. 15/5 = 3 mm c. (x, y) -> (x, -y); (x, y) -> (3x, y)