Mike DeVor. Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). _____________, Question 9. (x, y) -> (2x, 2y), Question 9. Jot down . Type below: B: Rotate the square 180 around the origin. How can you describe the effect of a dilation on coordinates using an algebraic representation?. For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates. (-6, 1), Question 13. Determine the coordinates of its image after a dilation with the given scale factor centered at the origin. (x, y) -> (x, -y) This is called a reduction. Represent Real-World Problems The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. In this unit we review the basic concept of a function and emphasize multiple representations of these foundational tools. y = 3x 1 _____________, Answer: List the coordinates of the vertices of the preimage in the first column of the table. F (3, 3) 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. Title: Microsoft Word - Document1 Author: lausd_user Created Date: 1/26/2015 2:42:29 PM . x = 3 C. Apply the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. algebraic rule: (x, y) -> (2/3x, 2/3y), Question 8. 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 . What is the scale factor in terms of inches to inches? ratio of x-coordinates = -4/-2 = 2 Type below: (show solution) Question 6 (request help) Critical Thinking A triangle has vertices A (-5, -4), B (2, 6), and C (4, -3). B: Rotate the square 180 around the origin. (2x, 2y) 5. Learning is not only important but understanding the concepts is also important for the students to enhance their skills. Represent Real-World Problems The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. Question 5. Type below: A dilation with center (0, 0) and scale factor k is applied to a polygon. 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? Type below: Perimeter = ________ units (-1, -1) The scale factor of the dilation is 2. Students use algebraic representations of dilations worksheet is a grid units. A(-5, -4) A'(3 (-5), 3 (-4)) A'(-15, -12) (1) Answer: a = 5, Question 5. For scale factor k, the algebraic representation of the dilation is (x, y) (kx, ky). Answer: The explanations seen in Go Math Grade 8 Answer Key Chapter 10 are prepared by the concerned subject experts. area = l.w = 2 . Type below: Area = ________ square units, Answer: D. Sketch the image after the dilation on the coordinate grid. _____________, Answer: horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. Type below: a. The blue square ABCD is the preimage. perimeter of the original square = 6 + 6 + 6 + 6 = 24 Explanation: Find the angle measures of the actual sign. _____________, Answer: Critical Thinking MNOP has vertices at M'(3, 4), N'(6, 4), O'(6, 7), and P'(3, 7). ratio of y-coordinates = ____________, Answer: What is the algebraic representation of this dilation? 3a = 15 Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. Explanation: b. a translation down 3 units 37, 53, and 90, Question 6. _____________, Answer: A'((3.-15), (3.-12)) -> A'(-15, -12) Answer: (x, y) (2.5x, 2.5y) The coordinates of the vertices of the original image are multiplied by \(\frac{1}{2}\) for the purple square. What is the scale factor for the dilation? The triangle ABC shown on the grid is the pre-image. S'(8.75, 6.25), a = 5, Question 5. Find the angle measures of the actual sign. The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals 2. All the explanations are given by the best online maths experts. velvet carpet for bedroom. e. What are the dimensions of the new room, in inches, on the blueprint? Type below: each side of the second figure is 1.25 times the corresponding side of the original figure. The homeowner wants this room to be 25% larger. Type below: Describe how the graph of y = x shown at the right is changed through each of the following transformations. Type below: When k is between 0 and 1, the dilation is a reduction by the scale factor k. _____________, Explanation: 2x = 6 (-4, -2), Question 12. Type below: 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. b. 130 0 obj <>stream Question 12. The vertices of the ditilated image are X'(1, 1), Y'(3, 3) and Z'(1, 3), Texas Go Math Grade 8 Lesson 13.2 Guided Practice Answer Key. Depending on the scale factor, dilation may increase or decrease the starting object. 10cm 40 = 400cm scale factor of \(\frac{1}{3}\) Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. The scale factor of the dilation is _______. The solution for this requires that you take the fifth root of both sides. _____________. _____________, Answer: The division process is straightforward. b. y = \(\frac{1}{3}\)x + 1 (4, 0) Perimeter = 2l + 2w = 2(2) + 2(2) = 8 Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Describe two transformations that will do this. d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Answer: _____________, Answer: a. a = -3 _____________, Answer: Total Meals Sent Learn More. (x, y) -> (2.5x, 2.5y) _____________, Answer: Time Squared Activity: Each participant gets 3 pages with 24 squares representing the hours in a day. (4, 0) The stage crewmembers calculation is incorrect. What dilation can you apply to the image to return it to the original preimage? x = 3 a. Graph the image. Section 10.1: Properties of Dilations. Answer: ratio of x-coordinates = 2 Mathematics. MN = \(\sqrt{(4.5)^{2}+(0)^{2}}\) Find the scale factor and the perimeter of each square. Type of function: Justification: 10. . Type below: Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? Then write an algebraic rule to describe the dilation. The scale factor k describes how much the figure is enlarged or reduced. (-2, 2) (7, 8) a. A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. (x, y) -> (1.5x, 1.5y) 4), (3.-3)) -> C'(12, -9), Question 7. 8cm 40 = 320cm Lets find the ratio oft: x-coordinates of corresponding points (0, 4) Type below: (2, -1) (0, -4) Scale factor: ________, Question 9. scale factor of 1.5 k = \(\frac{2}{3}\), Next, Let us represent the dilation algebraically, using B (7.5, 3) ________ inches d. A rectangular room has coordinates Q(2, 2), 6(7, 2), S(7, 5), and T(2, 5) on the blueprint. Identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3. A dilation can produce a larger figure or an enlargement or a smaller figure or a reduction. perimeter of the original square = 6 + 6 + 6 + 6 = 24 MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). Both Triangle S have Angle S of measures 38, 67 and 75. Graph the image of the figure using the transformation given. Yes; Quadrilateral DEFG is a dilation of quadrilateral DEFG. x = 3 Write the coordinates of the vertices of the preimage in the first column of the table. Scale factor: 2 a = 15/3 (0, -4) Options: Which represents the dilation shown where the black figure is the preimage? b. What is the effect on the figure when k > 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. (-5, 0) A dilation of the square has vertices at (6, 6), (6, 6), (6, 6), and (6, 6). The arrow shown is the preimage. Type below: (0, 4) 5/2 = 2.5 (x, y) -> (2.5x, 2.5y), Question 3. I (3, 6) LESSON 10-2 Practice and Problem Solving: A/B 1. The blueprints are plotted on a coordinate plane. Easily fill out PDF blank, edit, and sign them. Identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3. What is the scale factor for the dilation? The position of the sketch from 12A will be 1/2 unit above the sketch obtained when the translation occurs first. Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. ratio of y-coordinates = 4/2 = 2 Describe the transformations that will transform the image back into the original figure. Original perimeter: _________ horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. In Exercises 710, the transformation of a figure into its image is described. Then write an algebraic rule to describe the dilation. Answer: Both Triangle S have Angle S of measures 38, 67 and 75. c. The drawing has the hypotenuse on the bottom. Type below: What will the dimensions of the new room be, in feet, in the new house? The stage crewmembers calculation is incorrect. c. (x, y) -> (3x, 3y) Question 5. _____________, Answer: _____________, Answer: Page 338: Performance Tasks. Rotate the drawing 180 around the origin. The corresponding angles of triangle ABC and triangle ABC are congruent. Original perimeter: _________ Critical Thinking Explain how you can find the center of dilation of a triangle and its dilation. Sketch triangle ABC and ABC for the dilation (x, y) (-2x, 2y). (-7, -4) ratio of y-coordinates = 2/1 = 2 A(8, 0) A' . How does the dilation affect angle measures? 66`! S0\WbgU`U`6$ &m. Question 3. The blueprints are plotted on a coordinate plane. Justify your answer. length |QR| = |8.75 2.5| = 6.25 inch The center of dilation is the origin and (x, y) (3x, 3y). The scale factor is \(\frac{1}{4}\) Lets find the ratio of length \(\frac{20}{400}\) = \(\frac{1}{20}\) Type below: _____________, Answer: In the given expression, we can notice that the x coordinate is multiplied with \(\frac{2}{3}\). Answer: Type below: Type below: (-3, -4) a. The ratios of the lengths of the corresponding sides are not equal. Question 6. (-4, 3) dilation by scale factor of 3 (x, y) -> (3x, 3y) b. algebraic geometry, and planet motion; furthermore the system REDLOG is demonstrated and the verification of geometric statements as well as the automated production of proof in Euclidean Geometry are present. The first one is done for you. Type below: ADDITIONAL EXAMPLE 1. a. A'((3.-15), (3.-12)) -> A'(-15, -12) area = l.w = 8 .8 = 64, Question 6. 1/3x = 1 Answer: C: (x, y) (x 5, y 6) LJKG i 80`- wMK0,7 {1L`j7 Fi@W_w ~H; po0]uWuvGG]nB\9LgxG:1~}_ G 4. Divide a side length of the dilated figure by the corresponding side length of the original figure. The students can easily learn maths with the Go Math Grade 8 Solution Key. 62 3099-5574 R. Quintino Bocaiva, 359, Centro - Anpolis/GO . _____________, Answer: Multistep As with geometric figures, graphs can be transformed through translations, reflections, rotations, and dilations. Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? House dimensions: 25ft by 15ft, Question 10. Answer: coordinates for D Explain your reasoning. Scale factor: _________ Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? _____________, Answer: Question 12. x = 2 . 2x = 6 A square on the coordinate plane has vertices at (2, 2), (2, 2), (2, 2), and (2, 2). The figures are similar is they are the same shape but different size SO one is a dilation of the other, Question 11. 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 . LESSON 10-2 . horizontally shrinks by a factor of 2/3, Question 12. Explanation: Q'(2.5, 2.5), Area = 64 square units, Explanation: 4. What is the scale factor in terms of inches to inches? Type below: Is the crew members calculation correct if the painted replica is to cover the entire backdrop? b. 715 Module 20 Lesson 2 Algebraic Representation of Dilation DRAFT. After calculating the coordinates, we can graph every point of the image after dilation and connect them to get the wanted figure. c. a = 5 a. y = 2x + 6 C'((3. _____________, Question 12. Image perimeter: _________, Answer: 320, Algebraic Representations of Dilations Page No. Answer: Type below: d. a = 15, Explanation: Type below: ratio of y-coordinates = 4/2 = 2 coordinates for B Type below: MNOP has vertices at M(4.5, 6), N(9, 6), O'(9, 10.5), and P'(4.5, 10.5). original coordinates h2S0PP02]KsSJ Tu! e. What are the dimensions of the new room, in inches, on the blueprint? 21/7 = 3 mm (-1, 1) d. What are the perimeter and area of the image? x 2 Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. Complete Lesson 9 4 Algebraic Representations Of Transformations Answer Key online with US Legal Forms. Critical Thinking A dilation with center (0, 0) and scale factor k is applied to a polygon. c. a = 5 Type below: Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. _____________, Answer: Type below: _____________, Explanation: The figure is reflected across the y-axis and dilated by a scale factor of 4. _____________, Answer: The sides are proportional. When k is greater than 1, the dilation is an enlargement by the scale factor k. Question 5. _____________, Answer: Explain. 0 = -1/3 . (4, 0) x = 2 . _____________, Answer: a. Graph the image. algebraic rule: (x, y) -> (1/3x, 1/3y), Question 4. -4/-2 =2; 4/2 = 2 c. (x, y) -> (3x, 3y) Identify a sequence of two transformations that will transform figure A into the given figure. _____________, Answer: 2), (3.6)) -> B'(6, 18) Displaying all worksheets related to - Algebraic Representations Of Dilations. d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Explanation: CorrectionKey=B Transformations and Similarity MODULE 10 3. (x, y) -> (-x, y), Question 11. _____________, Answer: Worksheets are Middle school math series course 2, Chapter 7, Algebraic representations of dilations, Algebraic representations of dilations, Conjectures. Type below: Answer: C = (-2, -4), C = (-1, -2); You will have an extra practice for every lesson in the IM math program. > ~ y o The figures are similar is they are the same shape but different size SO one is a dilation of the other, Question 11. 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: Type below: _____________. y^m52p=Dupxm`>szry]-Ma!BH#0JT4X%`AcBM&1u)IQJS 9sNgql@IF2.P1 3u,P Answer: Find the scale factor and the perimeter of each square. d. y = 3x 1, Explanation: How does the dilation affect the length of line segments? A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) Original perimeter: _________ Sketch triangle ABC and ABC for the dilation (x, y) (-2x, -2y). Scale factor: _________ After dilation Type below: _____________, Explanation: ________ inches The blue square is the preimage. Options: 18/4 = 4.5 mm Question 7. Apply the indicated sequence of transformations to the square. What is the length of a side of the image? Texas Go Math Grade 8 Lesson 13.2 Explore Activity Answer Key. In Exercises 710, the transformation of a figure into its image is described. Find the scale factor and the perimeter of each square. Triangle XYZ has angles measuring 29 and 92. Critical Thinking MNOP has vertices at M(3, 4), N(6, 4), O(6, 7), and P(3, 7). (2, -2) Answer: Sketch triangle ABC and ABC for the dilation (x, y) (-2x, -2y). lesson 10 2 algebraic representations of dilationsasterisk sip reload not working. (-4, 4) (-2, 1) _____________, Explanation: Our services run deep and are backed by over ten years of experience. Perimeter = 2l + 2w = 2(8) + 2(8) = 32 (9, 6), (3, 6), (9, 3), (3, 3), Question 2. To create the actual sign shown, the drawing must be dilated using a scale factor of 40. (x, y) -> (1.5x, 1.5y) ratio of x-coordinates = -4/-2 = 2 _____________. Scale factor of 1.5 Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Which transformation in part c will accomplish this? coordinates for C (-7, -8) 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. 1/3x = 1 Examples, solutions, videos, worksheets, games, and activities to help geometry students learn. 8cm 40 = 320cm So, the scale factor is \(\frac{1}{20}\), and algebric rule of dilation is (x, y) (\(\frac{1}{20}\)x, \(\frac{1}{20}\)y) (-2.5, 2.5) figure C _____________, Answer: Explanation: The triangles have only one pair of congruent angles, Question 2. _____________, Explanation: ________ feet, Question 9. d. (x, y) -> (6x, 6y), Explanation: Question 2. The image is congruent to the original figure. D: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y) B: Rotate the square 180 around the origin. Scale factor: _________ Question 1. The figure is dilated by a factor of 2, but the orientation of the figure in the coordinate plane is rotated 180, Question 1. So, to learn maths in the best way, you must refer to HMH Go Math Grade 8 Solution Key.
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