BD/BD = 6/2 = 3 LESSON 10-2 Practice and Problem Solving: A/B 1. Multiply each coordinate of the vertices of rectangle FGHI by 1, 5 to find the vertices of the dilated image. Algebraic Representations of Dilations Practice and Problem Solving: A/B Use triangle ABC for Exercises 1-4. Triangle RST has angles measuring 38 and 75. (x, y) (kx, ky) 8cm 40 = 320cm 11,201. C'((3. Critical Thinking MNOP has vertices at M'(3, 4), N'(6, 4), O'(6, 7), and P'(3, 7). x = 2 . 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 _______. The center of dilation is the origin. G(5, 2) G'(5 1.5, 2 1.5) G'(7.5, 3) (2) Find the angle measures of the actual sign. What are the coordinates? The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals _______. B'(6, 18) (x, y) -> (1/4x, 1/4y) Worksheets are Algebraic representations of dilations, Correctionkeyb transformations and similarity module 10, Lesson algebraic representations of transformations 9 4, Do not edit changes must be made through file info, Pre algebra, Graph the image of the figure using the transformation, Ixl skill alignment, Unit . Area = 4 square units, Explanation: Type below: Lesson 2: Algebraic Representations of Dilations, Question 1. Type below: Which represents the dilation shown where the black figure is the preimage? _____________, Answer: _____________, Answer: OL@6BxtiJZ7f)^H(pjl4.I`'Fq rm;`$PE\!0P{a!-;}])o1Y-f /PMM$4x*gv|DeF. |_]prV8!Q~~p Displaying all worksheets related to - Lesson Algebraic Representation Of Dilations 102. (x, y) -> (1/5x, 1/5y), Question 10. Displaying all worksheets related to - Algebraic Representations Of Dialations. (-1, -1) Translate the image 3 units down and 6 units right and dilate it by a factor of 2 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. Multistep As with geometric figures, graphs can be transformed through translations, reflections, rotations, and dilations. (-2, 2) _____________, Answer: What is the algebraic representation of this dilation? Algebraic Representations of Dilations - 2. Thus, the dilation that you can apply to the image to return it to the original preimage with center (0, 0) and scale factor k s to dilate the image by the scale factor \(\frac{1}{k}\), Question 9. b. a translation down 3 units What are the vertices of the dilated image? After dilation coordinates for D Type below: After the sequencing of transformations, reflection over the y-axis. Question 5. d. (15, 10), (5, 10), (15, 5), (5, 5), Answer: c. What are the perimeter and area of the preimage? B'(6, 18) lesson 10 2 algebraic representations of dilations. Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? The triangles have only one pair of congruent angles, Question 2. c. y = \(\frac{2}{3}\)x 2 _____________. 21.1 Parallel Lines Cut by a Transversal. (-4, 4) a. Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. (-2, 0) 6cm 40 = 240cm MNOP has vertices at M(4.5, 6), N(9, 6), O'(9, 10.5), and P'(4.5, 10.5). . C'(12, -9), Explanation: Find the scale factor and the perimeter of each square. Type of function: Justification: 9. = 3 2 + 3. Question 2. HMH Into Math Grade 8 Module 2 Lesson 2 Answer Key Explore Dilations. C(-2, 4) C'( 2 (- 2), 2 4) C'(4, -8) . 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. 10-2. lesson. Solve a + 7 = 2a 8. Area = 4 square units, Explanation: 7. ratio of x-coordinates = _______ For 711, tell whether one figure is a dilation of the other or not. The coordinates of the vertices of the original image are multiplied by \(\frac{1}{2}\) for the purple square. The actual building measures 400 feet long and 320 feet high. b. The best learning comes with the best learning guide. Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. ratio of y-coordinates = ____________, Answer: Type below: 18/4 = 4.5 mm Identify a sequence of two transformations that will transform figure A into the given figure. ratio of y-coordinates = 2, Explanation: _____________, Answer: c. The drawing has the hypotenuse on the bottom. Reflection over x-axis (x, y) -> (x, -y) c. What are the perimeter and area of the preimage? 23 times. After calculating the coordinates, we can graph every point of the image after dilation and connect them to get the wanted figure. A'(-15, -12) _____________, Answer: ratio of x-coordinates = 2 Q'(2.5, 2.5), Answer: Scale factor: 2 Type below: Answer: letter of the transformation applied. _____________. b. horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. The corresponding angles of triangle ABC and triangle ABC are congruent. One inch on the blueprint represents how many inches in the actual house? This is a bundle of all first grade Illustrative Math-Friendly Units 1-8. A'((3.-15), (3.-12)) -> A'(-15, -12) Explanation: Echocardiography technique, Type below: d. y = 3x 1, Explanation: Type below: 326, Similar Figures Lesson Check Page No. Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. What will the dimensions of the new room be, in feet, in the new house? 21/7 = 3 mm perimeter of the original square = 6 + 6 + 6 + 6 = 24 Type below: _____________, Explanation: (7, 8) A = (-4, 4), A = (-2, 2); Time Squared Activity: Each participant gets 3 pages with 24 squares representing the hours in a day. a dilation produces an image similar to the original figure, Question 10. Answer: The backdrop scale factor is 1/20, not 1/12, Question 12. (x, y) (2.5x, 2.5y) MN = \(\sqrt{20.25}\) Type below: Type below: c. The drawing has the hypotenuse on the bottom. (x, y) -> (-y, x) _____________, Explanation: Highlight key terms and topics. Type below: x + 1 ratio of x-coordinates = -4/-2 = 2 The lengths are 240 cm, 320 cm, and 400 cm, Question 6. 324, Algebraic Representations of Dilations Page No. (x, y) (\(\frac{2}{3}\)x, y) c. (x, y) -> (3x, 3y) Type below: _____________, Answer: Transformations (including Dilations): 16.1 And 16.2 - Quizlet. Reflect the drawing over the x-axis coordinates for A (-7, -8) Perimeter = 8 units What is the algebraic representation of this dilation? meaning that we will multiply every coordinate with \(\frac{3}{2}\). x + 1 Explanation: MNPQ is not a dilation of MNPQ, Explanation: (2, -1) 320, Algebraic Representations of Dilations Page No. dilation with a scale factor of 0.5 A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) Describe what happens to a figure when the given sequence of transformations is applied to it: (x, y) (-x, y); (x, y) (0.5x, 0.5y); (x, y) (x 2, y + 2) Considering the fact that the y coordinate stayed the same and the fact that x coordinate is multiplied with a number smaller then 1, we can conclude that given figure is horizontally shrinked. 0 = -1/3 . b. Graph the image of each figure after a dilation with the origin as its center and the given scale factor. Scale factor: _________ _____________, Answer: Explain your reasoning. 10.2 Solving Exponential Equations - Intermediate Algebra. The figure is reflected across the y-axis and dilated by a scale factor of 4. ADDITIONAL EXAMPLE 1. Question 9. Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. B (7.5, 3) Mathematics. 4. 21.1 Parallel Lines Cut by a Transversal. coordinates for B So, the corresponding S are congruent. C(4, -3) C'(3 4, 3 (-3)) C'(12, -9) .. (3) 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: On a computer, Raquel uses polygons and a circle to make a model of the top of London's Big Ben clock . Write the algebraic representation of the dilation shown. 1. . ratio of y-coordinates = 4/2 = 2 A(0, 8), B(0, 0), C(10, 0) 3. a. Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? d. y = 3x 1, Explanation: Type below: Divide a side length of the dilated figure by the corresponding side length of the original figure. Question 6. Sketch triangle ABC and ABC for the dilation (x, y) (-2x, 2y). 1. H (7.5, 6) Question 7. _____________, Answer: perimeter of the image = 12 + 12 + 12 + 12 = 48, Question 20. A dilation of the square has vertices at (6, 6), (6, 6), (6, 6), and (6, 6). Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? How does the dilation affect angle measures? Question 2. _____________. 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 . (x, y) ( x, -y) Question 4. 4), (3.-3)) -> C'(12, -9), Question 7. Green square -> (x, y) -> (2x, 2y) 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 rectangle has vertices (6, 4), (2, 4), (6, 2), and (2, 2). Type below: 0 = 2/3 . B'((3. (0, -4) I Can identify and perform dilations given a scale factor and center of dilation, perform a dilation on a coordinate plane, and identify an algebraic rule for the dilation. A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). In this lesson, you will learn multiples of 11. B (7.5, 3) Answer: So, to learn maths in the best way, you must refer to HMH Go Math Grade 8 Solution Key. 325, Algebraic Representations of Dilations Lesson Check Page No. How many feet? class problems. perimeter of the image = 12 + 12 + 12 + 12 = 48, Question 20. (-2, 0) _____________. Therefore, MNPQ is not a dilation of MNPQ, Question 8. Find the lengths of the sides of the actual sign. The drawing has sides measuring 6 cm, 8 cm, and 10 cm, and angles measuring 37, 53, and 90. 77% average accuracy. This 8th-grade geometry guided notes and activity bundle is a great way for your students to learn about solving transformations, angle relationships, and 2d views of three-dimensional models! Displaying all worksheets related to - Algebraic Representations Of Dilations. (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y), Question 6. Identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3. Then write an algebraic rule to describe the dilation. Which equation does not represent a line with an x-intercept of 3? _____________. lesson 10 2 algebraic representations of dilations 12th June 2022 . Two triangles, Triangle 1 and Triangle 2, are similar. AB/AB = 2/4 = 1/2 perimeter of the original square = 6 + 6 + 6 + 6 = 24 -6/-3 =2; 6/3 = 2 \(\frac{1}{4}\) = \(\frac{1}{4}\) b. a translation down 3 units The business owner wants it to remain on the left after the hypotenuse goes to the top. _____________, Answer: Answer: Edit. CorrectionKey=B Transformations and Similarity MODULE 10 3. (-4, 3) When k is greater than 1, the dilation is an enlargement by the scale factor k. Question 5. House dimensions: 25ft by 15ft, Question 10. Question 7. a. Type below: h2V0Pw/+Q0L)0 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 _____________, Answer: 10/4 = 2.5 10cm 40 = 400cm Rotate the drawing 180 around the origin. 3x = 1 A stage crewmember writes (x, y) (\(\frac{1}{12}\)x, \(\frac{1}{12}\)y) to represent the dilation. Blueprint dimensions: 6.25 in. ________ feet, Question 9. (9, 6), (3, 6), (9, 3), (3, 3), Question 2. Then write an algebraic rule to describe the dilation. (-4, 4) (-1, 1) How can you find the scale factor of a dilation? algebraic rule of the dilation: (x, y) -> (1/4x, 1/4y), Question 11. Mod 20-2 Class Problems. ratio of y-coordinates = -4/-2 = 2, Question 2. G (7.5, 3) properties of dilations lesson 10-1 answer key, algebraic representations of dilations lesson 10-2 answers, lesson 17-1 dilations answers, lesson 17-1 practice dilations answers, lesson 10.1 properties of dilations answer key, lesson 11.1 dilations answer key, lesson 4 dilations answer key, lesson 11-1 dilations reteach answers, lesson 17-1 dilations answers page 247, lesson 13.1 properties of . Question 13. Write the coordinates of the vertices of the preimage in the first column of the table. Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. Type below: ________ feet, Question 9. Write the coordinates of some of the points on first graph: A(-2, 4), B(2, 4), C(0, -4), and on second graph: ________ inches The perimeter of the image is the perimeter of the original figure times the scale factor, Question 1. MN = \(\sqrt{(9-4.5)^{2}+(6-6)^{2}}\) ratio of y-coordinates = ____________, Answer: ________. a. Unit 9 Review. After dilation: k = \(\frac{3}{4.5}\) horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Question 4. Type below: d. A rectangular room has coordinates Q(2, 2), R(7, 2), S(7, 5), and T(2, 5) on the blueprint. This standard connects the work done with algebraic functions in grade 8 and Algebra I to geometric functions. Describe two transformations that will do this. (0, -4) (x, y) -> (2x, 2y), Question 9. b. To calculate the verticies of the image after dilation, we will use following rule: Type below: Apply the indicated sequence of transformations to the square. _____________. cfelg. _____________, Explanation: Notes. 2 Perrino 2011-11-28 The Practice of Perioperative Transesophageal Echocardiography provides over 100 teaching cases ranging from the most common to the most challenging. Type below: Type below: a = 5, Question 5. endstream endobj 133 0 obj <>stream d. What are the perimeter and area of the image? 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 _______. A stage crewmember writes (x, y) (\(\frac{1}{12}\)x, \(\frac{1}{12}\)y) to represent the dilation. Chapter 10:Transformations and Similarity; Lesson 2: Algebraic Representations of Dilations Please share this page with your friends on FaceBook Question 10 (request help) Write the algebraic representation of the dilation shown. -4/-2 =2; 4/2 = 2 Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. b. Answer: The angle measures are the same (-6, -1) figure C BD/BD = 6/2 = 3 ratio of y-coordinates = 2/1 = 2 Determine the coordinates of its image after a dilation with the given scale factor centered at the origin. Type below: h24T0P044P06R d. A rectangular room has coordinates Q(2, 2), R(7, 2), S(7, 5), and T(2, 5) on the blueprint. ratio of y-coordinates = 2/1 = 2 Describe two transformations that will do this. (x, y) -> (2.5x, 2.5y) _____________, Answer: lesson 10 2 algebraic representations of dilations class problems. The scale factor of the dilation is 2. Image perimeter: 48, Explanation: 8cm 40 = 320cm For 711, tell whether one figure is a dilation of the other or not. Algebraic Representations of Dilations Success for English Learners A dilation changes the size of a figure without changing its shape. _____________, Answer: (2, -1) All the explanations are given by the best online maths experts. 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. MN/MN = 3/4.5 = 2/3 Answer: a = 15/3 Draw Conclusions A figure undergoes a sequence of transformations that include dilations. (-2, -2) The figure and its final image are congruent. A dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction). MN/MN = 3/4.5 = 2/3 b. y = \(\frac{1}{3}\)x + 1 by cfelg. Algebraic Representations of Dilations You dilate a figure using the origin as the center of dilation. _____________, Answer: How would a dilation with scale factor 1 affect the preimage? Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity Online PDF to help the students to practice maths. Type below: Original perimeter: _________ Answer: Perimeter = ________ units The actual building measures 400 feet long and 320 feet high. (3, 2), (1, 2), (3, 1), (1, 1) coordinates for C Question 2. c. (x, y) -> (x, -y); (x, y) -> (3x, y) _____________, Answer: and find the ratio of heigh: \(\frac{16}{320}\) = \(\frac{1}{20}\) House dimensions: 25ft by 15ft, Question 10. Type below: What is the effect of a negative scale factor? I know that triangle ABC is a dilation of triangle ABC because the ratios of the corresponding x-coordinates are equal and the ratios of the corresponding y-coordinates are equal. This will be followed by the. lesson 10 2 algebraic representations of dilationsasterisk sip reload not working. Question 3. Describe the image of a dilation with a scale factor of 1. C = (-2, -4), C = (-1, -2); _____________, Answer: Perimeter = 2l + 2w = 2(8) + 2(8) = 32 The blueprint is the preimage and the house is the dilated image. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . The TEKS targeted in these notes are: 8.10(A) generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two dimensional shapes on a coordinate plane 8.10(B) differentiate between transformations that preserve congruence and those that do not 8.10(C) explain the effect of . 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. _____________, Answer: Learning is not only important but understanding the concepts is also important for the students to enhance their skills. We have provided the Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity in the pdf format so that you can practice in online and offline mode.