A'(-15, -12) a. Type below: The square is dilated under the dilation (x, y) (0.25x, 0.25y). (x, y) -> (-x, y); (x, y) -> (3x, 3y) _____________, Explanation: How can you use dilations to solve real-world problems? ratio of y-coordinates = 2, Explanation: Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. a = 5, Question 5. (x, y) -> (x +5, y-6), Question 3. 2 = 4. _____________. translation 2 units left and 2 units up, Question 6. _____________, Question 9. Type below: A(0, 2) A'(0, 4) The sides are proportional. Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? Answer: Then write an algebraic rule to describe the dilation. 8th grade. [GET] Lesson 10.2 Practice B Geometry Answers Pages 603-611 A 4 B 5 C 5.62 D 6.31 E 5.83 8. Quadrilateral MNPQ has side lengths of 15 mm, 24 mm, 21 mm, and 18 mm. (9, 6), (3, 6), (9, 3), (3, 3), Question 2. _____________. _____________, Explanation: For example, if the scale factor is "k", the algebraic representation of the dilation is For enlargements, k > 1 and for reductions, k 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: (x, y) -> (x, -y); (x, y) -> (3x, 3y), Question 4. Type below: To calculate the verticies of the image after dilation, we will use following rule: Green square -> (x, y) -> (2x, 2y) Coordinates after dilation Question 13. Green square -> (x, y) -> (2x, 2y) ______ units, Question 6. _____________, Answer: The center of dilation is the origin. ratio of y-coordinates = ____________, Answer: Answer: b. y = \(\frac{1}{3}\)x + 1 A: (x, y) (-x, y) a dilation produces an image similar to the original figure, Question 10. 8.10.C: Description: explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90, 180, 270, and 360 as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; and . x 2 coordinates for C Determine whether the given representation is representative of a linear, exponential, or quadratic function. Type below: Which equation does not represent a line with an x-intercept of 3? coordinates for B lesson 10 2 algebraic representations of dilations. Type below: What will the dimensions of the new room be, in feet, in the new house? Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. a. a = -3 (-4, -2) 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. 10.2 Algebraic Representations of Dilations. Edit. b. %PDF-1.6 % Image perimeter: 48, Explanation: How many feet? Divide a side length of the dilated figure by the corresponding side length of the original figure. lesson 10 2 algebraic representations of dilations Participants need to fill out: The first page . So, the corresponding S are congruent. Critical Thinking A dilation with center (0, 0) and scale factor k is applied to a polygon. 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. Type below: Scale factor: _________ (-1, -1), Question 6. House dimensions: 25ft by 15ft, Question 10. The coordinates of the vertices of the original image are multiplied by 2 for the green square. _____________, Answer: Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. (1, 1) Displaying all worksheets related to - Algebraic Representation Of Dialation. meaning that we will multiply every coordinate with \(\frac{3}{2}\). (x, y) (\(\frac{2}{3}\)x, y) The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals 2. Be the first person to grab Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity to score good marks in the exam. _____________, Answer: (-4, 2) y = -1/3 . \(\frac{1}{4}\) = \(\frac{1}{4}\) _____________. 332, Go Math Grade 5 Answer Key Pdf | Go Math 5th Grade Answer Key Pdf, McGraw Hill Math Grade 8 Lesson 21.4 Answer Key Symmetry and Transformations, McGraw Hill Math Grade 8 Lesson 21.3 Answer Key Circles, McGraw Hill Math Grade 8 Lesson 21.2 Answer Key Polygons, McGraw Hill Math Grade 8 Lesson 21.1 Answer Key Quadrilaterals, McGraw Hill Math Grade 8 Lesson 20.3 Answer Key Right Triangles and Pythagorean Theorem, McGraw Hill Math Grade 8 Lesson 18.2 Answer Key Line Segments and Rays, McGraw Hill Math Grade 8 Lesson 20.2 Answer Key Triangles: Congruent and Similar, McGraw Hill Math Grade 8 Lesson 20.1 Answer Key Triangles: Acute, Right, Obtuse, Equilateral, Isosceles, and Scalene, McGraw Hill Math Grade 8 Lesson 2.2 Answer Key Problem Solving, McGraw Hill Math Grade 8 Lesson 2.1 Answer Key Multiplying and Dividing Whole Numbers. What dilation can you apply to the image to return it to the original preimage? lesson 10 2 algebraic representations of dilationsbsn sports track order numberbsn sports track order number a. Since the center of dilation is (0, 0), you can simply divide all . _____________. Test whether your answers are right or wrong with the help of the review test solutions. Properties of Dilations Lesson Check Page No. Answer: Perimeter = ________ units (x, y) (-x, -y) Algebra Review. (x, y) -> (x+3, y+5), Question 5. _____________, Explanation: Question 5. (4, 0) 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 _______. Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. Answer: The triangles have only one pair of congruent angles, Question 2. b. e. What are the dimensions of the new room, in inches, on the blueprint? What is the effect of a negative scale factor? c. (x, y) -> (3x, 3y) 715 Module 20 Lesson 2 Algebraic Representation of Dilation DRAFT. 325. . y = 2/3 . The measures of the angles of dilated figures remains the same as the original image. You will have an extra practice for every lesson in the IM math program. _____________. The Go Math Grade 8 Solution Key Chapter 10 Transformations and Similarity help the students to enhance their math skills. ratio of y-coordinates = ____________, Answer: The grid shows a diamond-shaped preimage. Draw Conclusions A figure undergoes a sequence of transformations that include dilations. Critical Thinking MNOP has vertices at M(3, 4), N(6, 4), O(6, 7), and P(3, 7). MN = \(\sqrt{20.25}\) Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Triangle RST has angles measuring 67 and 38. Type below: (x, y) -> (1/3x, 1/3y), Question 8. 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. Explain how this can happen. ratio of y-coordinates = 2/1 = 2 (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y), Question 6. endstream endobj 133 0 obj <>stream The business owner wants it to remain on the left after the hypotenuse goes to the top. _____________. (x, y) -> (2.5x, 2.5y), Question 3. 10cm 40 = 400cm a. a dilation by a scale factor of 4 4. d. A rectangular room has coordinates Q(2, 2), 6(7, 2), S(7, 5), and T(2, 5) on the blueprint. (-3, -8) (x, y) (0.8x, 0.8y) (x, y) (0.5x, 1.5y) No; one figure is not a dilation of the other, Explanation: Answer: x = 3 Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. LESSON 10-2 Practice and Problem Solving: A/B 1. 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: Options: (-1, -1) Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). (x, y) (x, 2y) How does the dilation affect angle measures? What is the effect of a negative scale factor? Make a Conjecture (x, y) -> (1.5x, 1.5y) Write the algebraic representation of the dilation shown. Depending on the scale factor, dilation may increase or decrease the starting object. Type below: Example 10.2.1 Solve for in the equation . Identify a sequence of two transformations that will transform figure A into the given figure. One inch on the blueprint represents how many inches in the actual house? What are the vertices of the image? x = 3 _____________, Answer: ratio of x-coordinates = 2 a = 15/3 After dilation: Original perimeter: 24 The blue square is the preimage. ratio of x-coordinates = ____________ What is the algebraic representation of this dilation? Options: The homeowner wants this room to be 25% larger. _____________, Answer: About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . (-4, 2) A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) After the sequencing of transformations, reflection over the y-axis. Scale factor of 1.5 The figure is reflected across the y-axis and dilated by a scale factor of 4. H (7.5, 6) b. _____________, Answer: Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Which represents the dilation shown where the black figure is the preimage? Algebric rule of dilation will be (x, y) (\(\frac{1}{4}\)x, \(\frac{1}{4}\)y), Question 11. 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. h24T0P044P06R 5/2 = 2.5 Image perimeter: _________, Answer: Type below: The figure is dilated by a scale factor of 0.5 and translated 6 units left and 3 units up. Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). _____________, Answer: Question 1. For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates. S'(8.75, 6.25), Scale factor: 2 The best learning comes with the best learning guide. d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Answer: Graph the image of XYZ after a dilation with a scale factor of \(\frac{1}{3}\) and the origin as its center. Scale factor: ________, Question 9. The grid shows a diamond-shaped preimage. Question 12. 7. Question 7. The scale factor of the dilation is _______. 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. Algebraic Representations of Dilations Success for English Learners A dilation changes the size of a figure without changing its shape. _____________, Explanation: (0, 4) Graph the image of the figure using the transformation given. Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Answer: 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. 2), (3.6)) -> B'(6, 18) (Example 1). (x, y) -> (x, -y) a. a dilation by a scale factor of 4 b. No; the dilation is not the same reversed, Explanation: Since 1 foot = 12 inch, the scale factor is k = \(\frac{12}{\frac{1}{4}}\) = 48, b. ratio of y-coordinates = _______ What are the vertices of the dilated image? _____________. Explanation: Question 9. 8cm 40 = 320cm Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity Online PDF to help the students to practice maths. 324, Algebraic Representations of Dilations Page No. (5, 5) A (0, 4), B (0, 0), C (5, 0) 2. If the center of dilation is the origin and the scale factor is 3, graph the dilated image P'Q'R'. figure C d. (x, y) (\(\frac{2}{3}\)x, y) 1. 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. What is the effect on the figure when k > 1? (x, y) (x, 2y) Perimeter = 2l + 2w = 2(2) + 2(2) = 8 Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? A square on the coordinate plane has vertices at (2, 2), (2, 2), (2, 2), and (2, 2). height: |QT| = |6.25 2.5| = 3.75 inch b. a = \(\frac{1}{3}\) No; the dilation is not the same reversed, Explanation: 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 . -6/-3 =2; 6/3 = 2 (x, y) -> (2x, 2y), Question 9. The image is congruent to the original figure. Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. 23 times. ADDITIONAL EXAMPLE 1. Perimeter = 8 units 1. . Explain your reasoning. Lesson Video 20.2 . Which transformation in part c will accomplish this? Lesson 2: 20.2 Algebraic Representations of Dilations. The backdrop scale factor is 1/20, not 1/12, Question 12. d. y = 3x 1, Explanation: D: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y) ratio of y-coordinates = -4/-2 = 2, Question 2. Type below: The actual building measures 400 feet long and 320 feet high. (x, y) -> (2.5x, 2.5y), Question 3. a. b. a translation down 3 units b. a translation down 3 units What are the coordinates? C = (-2, -4), C = (-1, -2); T'(2.5, 6.25), Question 9. The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. Area = ________ square units, Answer: _____________, Answer: Page 333: Ready to Go On? Both Triangle S have Angle S of measures 38, 67 and 75. Represent Real-World Problems The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. _____________, Answer: Scale factor: _________ d. (x, y) (\(\frac{2}{3}\)x, y) (-4, -2) Dilate each figure with the origin as the center of dilation. (1, 1) A rectangle has vertices (6, 4), (2, 4), (6, 2), and (2, 2). Page 335: Study Guide Review: Module 9. Transformations (including Dilations): 16.1 And 16.2 - Quizlet. 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 . Question 4. (-5, 0) ratio of x-coordinates = -2/-1 = 2 Type of function: Justification: 10. . The blue square is the preimage. _____________, Explanation: What is the length of a side of the image? How does the dilation affect the length of line segments? (x, y) -> (1.5x, 1.5y) 77% average accuracy. Critical Thinking Explain how you can find the center of dilation of a triangle and its dilation. Triangle XYZ has angles measuring 54 and 29. (0, -4) A(0, 8), B(0, 0), C(10, 0) 3. scale factor of \(\frac{1}{3}\) Firstly, we will write the coordinates of the vertices of the preimage. \(\frac{-\frac{1}{2}}{-2}=\frac{\frac{1}{2}}{2}=\frac{1}{4}\) A dilation of the square has vertices at (6, 6), (6, 6), (6, 6), and (6, 6). 0 = 2/3 . If two figures are similar but not congruent, what do you know about the sequence of transformations used to create one from the other? x = 1/3, Question 6. b. Save. AB/AB = 6/2 = 3 (x, y) -> (-x, y); (x, y) -> (3x, 3y) Determine whether one figure is a dilation of the other. On a coordinate plane, triangle UVW has coordinates U(20, 12), V(8, 6), and W(24, -4). What is the algebraic representation of this dilation? Some dilations are reductions. In Exercises 710, the transformation of a figure into its image is described. Perform a dilation on the coordinate plane. Explain. The corresponding angles of triangle ABC and triangle ABC are congruent. Texas Go Math Grade 8 Lesson 13.2 Explore Activity Answer Key. Multiply each coordinate by the scale . During the video lesson have students: Take notes on the material. (-2, 0) Give the coordinates of each vertex of ABC. (-2, 0) d. What are the perimeter and area of the image? H (7.5, 6) _____________, Question 9. 10/4 = 2.5 146 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 . _____________. C. Apply the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. Sketch triangle ABC and ABC for the dilation (x, y) (-2x, 2y). c. What are the perimeter and area of the preimage? perimeter of the original square = 4 + 4 + 4 + 4 = 16 dilations map a line segment (the preimage) to another line segment whose length is the product of the scale factor and the length of the preimage Dilation Property #6 dilations map a line not passing through the center of dilation to a parallel line and leave a line passing through the center unchanged k= image over preimage . C(4, -3) C'(3 4, 3 (-3)) C'(12, -9) .. (3) d. (x, y) -> (6x, 6y), Explanation: 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) Question 2. Scale factor: ________, Question 9. This is a bundle of all first grade Illustrative Math-Friendly Units 1-8. ratio of x-coordinates = 4/2 = 2 scale factor of \(\frac{1}{3}\) ________ feet, Question 9. Question 4. Scale factor = 2 vertically stretches by a factor of 2, Question 12. original coordinates d. (15, 10), (5, 10), (15, 5), (5, 5), Answer: Dilate each figure with the origin as the center of dilation. 5/2 = 2.5 _____________, Answer: Perimeter = ________ units Each case is succinctly presented in an easy-to-read question-answer, self-test format comprised of three printed pages of text and echo images. Area = ________ square units, Answer: 10-2. lesson. What will the dimensions of the new room be, in feet, in the new house? The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals _______. by 3.75 in. Answer: Let x and y be the coordinates of the original image When a dilation n the coordinate plane has the origin as the center of dilation, you can find points on the dilated image by multiplying the x- and y-coordinates of the original figure by the scale factor k, that is (x, y) -> (1.5x, 1.5y) ratio of y-coordinates = 4/2 = 2 Graph the image of the figure using the transformation given. Echocardiography technique, Question 2. MN/MN = 3/4.5 = 2/3 21/7 = 3 mm (-7, -8) (x, y) (\(\frac{2}{3}\)x, \(\frac{2}{3}\)y). A: (x, y) (-x, y) H(5, 4) H'(5 1.5, 4 1.5) H'(7.5, 6) (4) Mike DeVor. Type below: List the coordinates of the vertices of the preimage in the first column of the table. and the ratio of the y-coordinates of corresponding points 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. Identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3. class problems. _____________, Answer: B(-2, 1) B'( 2 ( 2), 2 1) B'(4, -2) .. (2) The figure shown on the grid is the preimage. Perimeter = 32 units A dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction). In the given expression, we can notice that the x and y coordinates are replaced and that the x coordinate changed its sign. (0, 4) (-4, 3) (-4, 0), Question 4. Explanation: coordinates for A C'(12, -9), Explanation: (0, -4) Yes; Quadrilateral DEFG is a dilation of quadrilateral DEFG. . Quadrilateral MNPQ has side lengths of 15 mm, 24 mm, 21 mm, and 18 mm. Type below: The stage crewmembers calculation is incorrect. What is the scale factor in terms of inches to inches? (x, y) -> (-x, y); (x, y) -> (x, 3y) Type below: B (7.5, 3) (1, -1). Question 6. Problem 1 What are the characteristics of an enlargement? 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. endstream endobj 136 0 obj <>stream D. Sketch the image after the dilation on the coordinate grid. 10/4 = 2.5 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. Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Explanation: Explain your reasoning. The center of dilation is the origin and (x, y) (3x, 3y). Reflect the drawing over the x-axis 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 _______. Determine whether one figure is a dilation of the other. The angle measures are the same After dilation 130 0 obj <>stream To create the actual sign shown, the drawing must be dilated using a scale factor of 40. _____________, Question 9. y = -2x + 6 After dilation Triangle RST has angles measuring 67 and 38. All the explanations are given by the best maths experts. Orientation of the figure in the coordinate plane is rotated 180. A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). In Exercises 710, the transformation of a figure into its image is described. perimeter of the image = 8 + 8 + 8 + 8 = 32, Question 20. The figure and its final image are congruent. The corresponding angles of triangle ABC and triangle ABC are congruent. Answer: y^m52p=Dupxm`>szry]-Ma!BH#0JT4X%`AcBM&1u)IQJS 9sNgql@IF2.P1 3u,P . 15/5 = 3 mm area = l.w = 2 . Since it changes the size of a figure, it has no something to do with the changes when it comes to the angles of the image.
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