lesson 10 2 algebraic representations of dilations

The ratios of the lengths of the corresponding sides are not equal. G (7.5, 3) d. y = 3x 1, Explanation: Apply each transformation to the image of the previous transformation. Image perimeter: 32, Explanation: (x, y) (0.8x, 0.8y) The figure shown on the grid is the preimage. hdPn0d $RE=LCR!cVmPH%K "?/2OGO7}`+ % R9}t$9plj`H:nH!Q)"p.4jb sH?yu_^DX ro)B \F}c]y?aGC_j>m3TF}};{{L;?O 5^dI 320, Algebraic Representations of Dilations Page No. Type below: Question 2. coordinates for C D: (x, y) ($\frac{1}{2}$x, $\frac{1}{2}$y) Test whether your answers are right or wrong with the help of the review test solutions. Options: Multiple Choice Use the diagram below to find the value of x. . Type below: The scale factor is $\frac{1}{4}$ (-3, -4) MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). Type below: Complete Lesson 9 4 Algebraic Representations Of Transformations Answer Key online with US Legal Forms. figure C Divide a side length of the dilated figure by the corresponding side length of the original figure. Type below: Substituting the value of k Type below: Multiply each coordinate of the vertices of ABC by 3 to find the vertices of the dilated image. (x, y) -> (x+6, y-3) Type below: Type below: _____________, Answer: a = 5, Question 5. dilation by scale factor of 3 (x, y) -> (3x, 3y) (5, 5) Question 12. (x, y) ($\frac{2}{3}$x, $\frac{2}{3}$y). H (7.5, 6) Question 1. 715 Module 20 Lesson 2 Algebraic Representation of Dilation. _____________. The blue square is the preimage. y^m52p=Dupxm`>szry]-Ma!BH#0JT4X%`AcBM&1u)IQJS 9sNgql@IF2.P1 3u,P No; one figure is not a dilation of the other, Explanation: (x, y) -> (1/4x, 1/4y) Displaying all worksheets related to - Algebraic Representations Of Dialations. MN = $\sqrt{(3)^{2}+(0)^{2}}$ Type below: Describe two transformations that will do this. (x, y) -> (2.5x, 2.5y), Question 3. R'(8.75, 2.5), On a coordinate plane, triangle UVW has coordinates U(20, 12), V(8, 6), and W(24, -4). Type below: The figure is dilated by a scale factor of 0.5 and translated 6 units left and 3 units up. (-4, 2) b. y = $\frac{1}{3}$x + 1 20.3 Similar Figures. Green square -> (x, y) -> (2x, 2y) _____________, Answer: _____________, Answer: Which transformation in part c will accomplish this? Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). 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. Image perimeter: _________, Answer: Notes. Image perimeter: _________, Answer: Problem 1 What are the characteristics of an enlargement? h2W0P+-60rb X;; | Section 10.2: Algebraic Representation of Dilations. For 711, tell whether one figure is a dilation of the other or not. x = 2 . A(0, 2) A'(0, 4) Represent Real-World Problems The blueprints for a new house are scaled so that $\frac{1}{4}$ inch equals 1 foot. (-2, -2), Question 12. (0, -3) Type below: What is the scale factor in terms of inches to inches? Question 1. Multiply each coordinate of the vertices of rectangle FGHI by 1, 5 to find the vertices of the dilated image. Explain how this can happen. Quadrilateral MNPQ has side lengths of 5 mm, 8 mm, 7 mm, and 4 mm. c. What are the perimeter and area of the preimage? )X}Dh=64z!vv 8 Type below: Then write an algebraic rule to describe the dilation. Graph the image of the figure using the transformation given. (-2, 2) )ABC 324, Algebraic Representations of Dilations Page No. So, the scale factor of the dilation is 3/4. Highlight key terms and topics. Answer: _____________, Answer: Type below: (-4, 2) (-4, 3) Scale factor: 2 (x, y) -> (x, y+6) Triangle XYZ has angles measuring 29 and 92. a. 326, Similar Figures Lesson Check Page No. -a + 7 = 2a 8 https://www.emathinstruction.com . The Organic Chemistry Tutor. The blue square is the preimage. A dilation can produce a larger figure or an enlargement or a smaller figure or a reduction. _____________, Answer: 15/5 = 3 mm What dilation can you apply to the image to return it to the original preimage? Answer: Dilation is a process of changing the size of an object while the object remains in the same Shape. Scale factor: ________, Question 9. Displaying all worksheets related to - Algebraic Representations Of Dilations. (9, 6), (3, 6), (9, 3), (3, 3) Type below: The blueprints are plotted on a coordinate plane. Type below: algebraic rule of the dilation: (x, y) -> (1/4x, 1/4y), Question 11. 13.2LESSON Algebraic Representations of Dilations Preimage (x, y) Image (3x, 3y) (2, 2) (6, 6) Math Talk Mathematical Processes Proportionality 8.3.C Use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of . Represent Real-World Problems The blueprints for a new house are scaled so that $\frac{1}{4}$ inch equals 1 foot. A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) How can you use dilations to solve real-world problems? 325. . (-6, 1), Question 13. Type below: b. Question 9. 2a + a = 8 + 7 Then write them algebraically. 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) For enlargements, k > 1. After dilation 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. Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. DRAFT. MN = 4.5, Length of MN, given M'(3, 4), N'(6, 4). Our services run deep and are backed by over ten years of experience. Explanation A: ALGEBRAIC REPRESENTATIONS OF DILATIONS WORKSHEET Problem 1 : The triangle PQR shown on the grid is the pre-image. coordinates for B MN = $\sqrt{9}$ How can you find the scale factor of a dilation? (1, -1) Reflect the drawing over the x-axis D. Sketch the image after the dilation on the coordinate grid. 13.2. Answer: Draw Conclusions A figure undergoes a sequence of transformations that include dilations. Question 4. each side of the second figure is 1.25 times the corresponding side of the original figure. h27P0P0P02V0T05U0R0QP0J'A@PE0I8tc ! Question 6. 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. Graph the dilation. Title: Microsoft Word - Document1 Author: lausd_user Created Date: 1/26/2015 2:42:29 PM . Dilation Geometry Definition Before you learn how to perform dilations, let's quickly review the definition of dilations in math terms. (x, y) (y, -x) 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: 10/4 = 2.5 (x, y) -> (-x, y); (x, y) -> (x, 3y) What are the coordinates? scale factor = 3, Explanation: (-2, 2) 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. For scale factors between 0 and 1, the image is smaller than the preimage. What is the algebraic representation of this dilation? perimeter of the original square = 4 + 4 + 4 + 4 = 16 (x, y) -> (x +5, y-6), Question 3. hWKo@+{"eA"EmUQF &; q8|y<>&Bad velvet carpet for bedroom. (x, y) -> (2.5x, 2.5y) 2/3x = 2 The figures are similar is they are the same shape but different size SO one is a dilation of the other, Question 11. Answer: c. (12, 8), (4, 8), (12, 4), (4, 4) Question 3. Question 16. 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. Question 13. 324, Algebraic Representations of Dilations Page No. ratio of y-coordinates = 4/2 = 2 G (7.5, 3) Length of MN, given M(4.5, 6), N(9, 6). (0, -4) What are the vertices of the image? Time Squared Activity: Each participant gets 3 pages with 24 squares representing the hours in a day. Type below: _____________, Answer: ________ inches _____________, Explanation: Question 4. (9, 6), (3, 6), (9, 3), (3, 3) (-2, 0) ratio of y-coordinates = 2/1 = 2 d. (x, y) ($\frac{2}{3}$x, y) _____________, Answer: Identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3. (4, 0) _____________. -6/-3 =2; 6/3 = 2 If the scale factor k is between 0 and 1 the image is a reduction. Type below: The homeowner wants this room to be 25% larger. Type below: Answer: a. Graph the image. 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. (x, y) ($\frac{2}{3}$x, y) Algebraic Representations Of Dialations Worksheets - total of 8 printable worksheets available for this concept. Perimeter = 2l + 2w = 2(8) + 2(8) = 32 To calculate the verticies of the image after dilation, we will use following rule: Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. Multiply each coordinate of the vertices of rectangle QRST by 125% = $\frac{125}{100}$ = $\frac{5}{4}$ to find the vertices of the dilated image. lesson 10 2 algebraic representations of dilationsppl center view from my seatppl center view from my seat Original perimeter: 16 (1, 1) Describe how the graph of y = x shown at the right is changed through each of the following transformations. Options: Type below: Type below: Which represents the dilation shown where the black figure is the preimage? AB/AB = 2/4 = 1/2 _____________. Question 6. 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. (-5, 0) 1. Your service title Give us a brief description of the service that you are promoting. d. (15, 10), (5, 10), (15, 5), (5, 5), Answer: House dimensions: 25ft by 15ft, Question 10. _____________. (x, y) -> (-y, x) (-4, 2) Type below: Type below: Type below: (0, 4) a = 15/3 (-4, -2) Identify a sequence of two transformations that will transform figure A into the given figure. C: (x, y) (x 5, y 6) a. a = -3 Answer: B: Rotate the square 180 around the origin. 62 3099-5574 R. Quintino Bocaiva, 359, Centro - Anpolis/GO . B. 8th grade. Participants need to fill out: The first page . ADDITIONAL EXAMPLE 1. ratio of y-coordinates = -4/-2 = 2, Question 2. 2 = 4. 10 x 10 = 7 x 2 = 10 x 9 = 5 x 8 = 10 x 3 = How did you do? The figure is reflected across the x-axis and dilated by a scale factor of 3. When k is between 0 and 1, the dilation is a reduction by the scale factor k. (-4, 0), Question 4. C (7.5, 6) Date Class LESSON Algebraic Representations of Dilations Reteach You dilate a figure using the origin as the center of . (x, y) (y, -x) by 3.75 in. horizontally shrinks by a factor of 2/3, Question 12. Coordinates after dilation # $ % &. Write the algebraic representation of the dilation shown. Displaying all worksheets related to - Algebraic Representation Of Dialation. endstream endobj 134 0 obj <>stream Properties of Dilations Lesson Check Page No. Type below: Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Perimeter = 8 units The business owner would like it on the top. Q'(2.5, 2.5), C = (-2, -4), C = (-1, -2); d. A rectangular room has coordinates Q(2, 2), 6(7, 2), S(7, 5), and T(2, 5) on the blueprint. How does the dilation affect the length of line segments? perimeter of the image = 12 + 12 + 12 + 12 = 48, Question 20. Triangle UVW has coordinates U(15, 9), V(6, 4.5), and W(18, -3). 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. 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. Original perimeter: _________ ADDITIONAL EXAMPLE 1 Graph the image of rectangle JKLM after a dilation with the origin as its center and a scale factor of 2. Explain your reasoning. Explanation: Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. What is the scale factor for the dilation? -a + 7 = 2a 8 C: (x, y) (x 5, y 6) 325, Algebraic Representations of Dilations Lesson Check Page No. Original perimeter: _________ vertically stretches by a factor of 2, Question 12. community surgical supply lawsuit; . Question 7. Type below: Determine whether one figure is a dilation of the other. Mod 20-2.mp4. 1/3x = 1 Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. *Click on Open button to open and print to worksheet. Type below: Mod20-2Notes. (-6, -2) _____________, Answer: (3, 8) What is the effect of a negative scale factor? LJKG i 80`- wMK0,7 {1L`j7 Fi@W_w ~H; po0]uWuvGG]nB\9LgxG:1~}_ G ratio of y-coordinates = _______ The first one is done for you. 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. _____________. Let us determine the dilation than can be applied to the image to return it to the original preimage. For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates. _____________. A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). area = l.w = 8 .8 = 64, Question 6. b. 0 = -2x + 6 Question 3. In Exercises 710, the transformation of a figure into its image is described. Download Go Math Grade 8 Chapter 10 Transformations and Similarity Answer Key PDF and begin your practice. The HMH Go Math 8th Grade Chapter 10 Transformations and Similarity Solution Key includes properties of dilations, Algebraic Representations of Dilations, and similar figures. Triangle RST has angles measuring 67 and 38. 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. Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Type below: Lesson 16 - Combining Dilations (Notes, Key) 10. _____________, Answer: Answer: (x, y) ($\frac{1}{2}$x, $\frac{1}{2}$y), Question 6. 'LODWLRQV3UDFWLFH 6. (-4, 2) R'(8.75, 2.5), (-1, -1) f& Type below: Page 335: Study Guide Review: Module 9. Question 5. x = 3 Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). by cfelg. (-1, -1) Type below: _____ Answer: Green square -> (x, y) -> (2x, 2y) (x, y) -> (x+6, y-3) Type below: (0, 4) (x, y) -> (2.5x, 2.5y) The corresponding angles of triangle ABC and triangle ABC are _______. Make a Conjecture Lesson Video 20.2 . _____________. -4/-2 =2; 4/2 = 2 D: (x, y) ($\frac{1}{2}$x, $\frac{1}{2}$y) Type below: (show solution) Question 6 (request help) Critical Thinking A triangle has vertices A (-5, -4), B (2, 6), and C (4, -3). (-1, -1) c. (x, y) -> (x, -y); (x, y) -> (3x, y) H (7.5, 6) MN = $\sqrt{(9-4.5)^{2}+(6-6)^{2}}$ Filled table is shown in the picture below. What are the coordinates of the new room? _____________. Save. 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. x + 1 _____________, Answer: scale factor of $\frac{1}{3}$ Classify each as such and justify your reasoning. The students can easily learn maths with the Go Math Grade 8 Solution Key. Explain. The division process is straightforward. -4/-2 =2; 4/2 = 2 The center of dilation is the origin and (x, y) (3x, 3y). _____________, Answer: Texas Go Math Grade 8 Lesson 13.2 Explore Activity Answer Key. The HMH Go Math 8th Grade Chapter 10 Transformations and Similarity Solution Key includes properties of dilations, Algebraic Representations of Dilations, and similar figures. (-2.5, 2.5) 10/4 = 2.5 Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. Algebraic Representation Of Dialation | Lesson 2 22 | Cryptic Quiz Page 41 | Count Classify Furniture | Weeky Math Review Q32 | Memo Types | 3 Letter Notation | Math P3 | Inferencing 3 | The Arthritis Menace Reading Answer | R 10 8 | Fragments And Sentences | Nothing Details | Gina Wilson Answer Key | Statistics Grade 1 | Persuasive Language . F (3, 3) Unit 9 Review. . Answer: The dilation should be centered at 9, negative 9, and have a scale factor of 3. 0 = 3x 1 (7, 4) Graph the image of XYZ after a dilation with a scale factor of $\frac{1}{3}$ and the origin as its center. perimeter of the original square = 6 + 6 + 6 + 6 = 24 What is the effect on the figure when k > 1? Quadrilateral MNPQ is the same shape but a different size than quadrilateral MNPQ. _____________, Answer: A rectangle has vertices (6, 4), (2, 4), (6, 2), and (2, 2). Answer: b. Explanation: List the coordinates of the vertices of the preimage in the first column of the table. (-2, 0) Write the algebraic representation of the dilation shown. 2), (3.6)) -> B'(6, 18) If you draw a line connecting each pair of corresponding vertices, the lines will intersect at the center of dilation, Question 20. (-1, -1), Question 6. Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. ratio of y-coordinates = 2/1 = 2 0 = 2/3 . (-3, -8) a. _____________, Answer: Triangle XYZ has angles measuring 29 and 92. Describe the transformations that will transform the image back into the original figure. figure B Answer: Write the algebraic representation of the dilation shown. a = 15/3 y = 3x 1 The Go Math Grade 8 Solution Key Chapter 10 Transformations and Similarity help the students to enhance their math skills. (x, y) (2.5x, 2.5y) The square is dilated under the dilation (x, y) (0.25x, 0.25y). Dilate each figure with the origin as the center of dilation. What is the effect on the figure when k > 1? coordinates for A A (0, 4), B (0, 0), C (5, 0) 2. A stage crewmember writes (x, y) ($\frac{1}{12}$x, $\frac{1}{12}$y) to represent the dilation.