lesson 10 2 algebraic representations of dilations

A dilation of the square has vertices at (6, 6), (6, 6), (6, 6), and (6, 6). ratio of x-coordinates = -4/-2 = 2 y^m52p=Dupxm`>szry]-Ma!BH#0JT4X%`AcBM&1u)IQJS 9sNgql@IF2.P1 3u,P 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. The sides are proportional. lesson 10 2 algebraic representations of dilationsppl center view from my seatppl center view from my seat _____________, Explanation: _____________, Answer: Then write an algebraic rule to describe the dilation. What is the algebraic representation of this dilation? The stage crewmembers calculation is incorrect. ratio of x-coordinates = ____________ The dimension of a new room on a blueprint is now: Mod20-2Notes. Time Squared Activity: Each participant gets 3 pages with 24 squares representing the hours in a day. 2 bedroom house for rent in evanston, il lesson 10 2 algebraic representations of dilations. Then write an algebraic rule to describe the dilation. coordinates for D 325, Algebraic Representations of Dilations Lesson Check Page No. x + 1 Dilate the image by a factor of 1/4 and reflect it back across the y-axis. Original perimeter: 24 2x = 6 Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. Perimeter = 32 units How many feet? 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. hWKo@+{"eA"EmUQF &; q8|y<>&Bad b. a = $\frac{1}{3}$ 20.3 Similar Figures. f& 90 clockwise rotation, Question 12. The business owner wants it to remain on the left after the hypotenuse goes to the top. _____________, Answer: Eureka Math Algebra 1 Module 2 Lesson 1 Answer Key; Eureka Math Algebra 1 Module 2 Lesson 2 Answer Key; Eureka Math Algebra 1 Module 2 Lesson 3 Answer Key . 325. . velvet carpet for bedroom. 8cm 40 = 320cm Explain your reasoning. Determine the coordinates of its image after a dilation with the given scale factor centered at the origin. _____________, Question 9. Scale factor = 2 c. (12, 8), (4, 8), (12, 4), (4, 4) y = 3x 1 3a = 15 C'(12, -9), Explanation: Image perimeter: 48, Explanation: MN = $\sqrt{20.25}$ Justify your answer. Dilate the image by a factor of 1/4 and reflect it back across the y-axis. Scale factor = 2 Question 12. (-4, 4) _____________, Question 9. houses for sale chepstow moon and co. shani hardwick wilson obituary A (3, 3) Page 333: Ready to Go On? Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity Online PDF to help the students to practice maths. (x, y) -> (x +5, y-6), Question 3. horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. endstream endobj 137 0 obj <>stream vertically stretches by a factor of 2, Question 12. ratio of y-coordinates = 4/2 = 2 B. _____________, Question 12. (0, -3) 0 = -2x + 6 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 . -a + 7 = 2a 8 So, the corresponding S are congruent. Type below: Find the lengths of the sides of the actual sign. 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. perimeter of the original square = 6 + 6 + 6 + 6 = 24 and find the ratio of heigh: $\frac{16}{320}$ = $\frac{1}{20}$ (-2, 1) _____________, Answer: h27P0P0P02V0T05U0R0QP0J'A@PE0I8tc ! 2/3x = 2 The backdrop scale factor is 1/20, not 1/12, Question 12. 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. How does the dilation affect angle measures? _____________. (9, 6), (3, 6), (9, 3), (3, 3) a = 15/3 _____________, Answer: ratio of x-coordinates = _______ D. Sketch the image after the dilation on the coordinate grid. Scale factor: ________, Question 9. Type below: (0, -4) (4, 0) The scale factor of the dilation is _______. The blueprint is the preimage and the house is the dilated image. (x, y) (kx, ky) (-2, 2) (-6, 1), Question 13. ! " c. y = $\frac{2}{3}$x 2 Triangle RST has angles measuring 67 and 38. _____________, Answer: A = (-4, 4), A = (-2, 2); Graph the image of XYZ after a dilation with a scale factor of $\frac{1}{3}$ and the origin as its center. C. Apply the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. facial recognition time clock no monthly fee; mower deck spindle replacement B. coordinates for C Answer: Apply each transformation to the image of the previous transformation. H (7.5, 6) coordinates for B Filled table is shown in the picture below. by 3.75 in. Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. 1/3x = 1 Dilation is defined as a transformation that changes the size of a figure. After dilation: y = -2x + 6 Answer: Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). Type below: LJKG i 80`- wMK0,7 {1L`j7 Fi@W_w ~H; po0]uWuvGG]nB\9LgxG:1~}_ G _____________. c. a = 5 A'(-15, -12), B'(6, 12) and C'(12, -9). Multiply each coordinate by the scale . The scale factor of the dilation is 2. (4, 0) Type below: d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Explanation: Answer: 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. Type below: Download Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity pdf for free of cost. On a coordinate plane, triangle UVW has coordinates U(20, 12), V(8, 6), and W(24, -4). x = 1/3, Question 6. In feet 6.25 4 = 25ft and 3.75 4 = 15 ft, Question 10. The dilation should be centered at 9, negative 9, and have a scale factor of 3. (-2, 1) A (3, 3) A dilation of (x, y) (kx, ky) when 0 < k < 1 has what effect on the figure? (-2, 0) scale factor of 1.5 A dilation of the square has vertices at (6, 6), (6, 6), (6, 6), and (6, 6). If you draw a line connecting each pair of corresponding vertices, the lines will intersect at the center of dilation, Question 20. MN = 4.5, Length of MN, given M'(3, 4), N'(6, 4). Section 10.2: Algebraic Representation of Dilations. lesson 10 2 algebraic representations of dilations 12th June 2022 . Type below: h2W0P+-60rb X;; | algebraic rule: (x, y) -> (1/3x, 1/3y), Question 4. Name:&_____& &&&&&Date:&_____& Lesson:'10.2'Algebraic'Representations'of'Dilations'' Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. Easily fill out PDF blank, edit, and sign them. (-2, 2) Type below: 0. d. (x, y) -> (6x, 6y), Explanation: _____________, Answer: Type below: translation 2 units left and 2 units up, Question 6. The figure is dilated by a scale factor of 0.5 and translated 6 units left and 3 units up. Answer: 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 Type below: What is the effect on the figure when k > 1? The center of dilation is the origin. Answer: (x, y) (x, 2y) (-5, 0) Question 4. The sides are proportional. figure C C: (x, y) (x 5, y 6) Options: Write the coordinates of the vertices of the preimage in the first column of the table. The first one is done for you. Type below: 10/4 = 2.5 Area = 4 square units, Explanation: _____________, Answer: _____________, Answer: 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: a. Graph the image. ________ feet, Question 9. (-1, -1), Question 6. Explain how this can happen. Coordinates after dilation Rotate the drawing 180 around the origin. (2, 2) Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. The arrow shown is the preimage. d. The shorter leg of the drawing is currently on the left. ratio of x-coordinates = -2/-1 = 2 Answer: a. c. y = $\frac{2}{3}$x 2 C. Apply the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. x = 1/3, Question 6. At least one transformation must be a dilation with a scale factor other than 1, Question 6. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . Coordinates after dilation Participants need to fill out: The first page . _____________, Answer: Therefore, MNPQ is not a dilation of MNPQ, Question 8. Examples, solutions, videos, worksheets, games, and activities to help geometry students learn. H(5, 4) H'(5 1.5, 4 1.5) H'(7.5, 6) (4) After dilation: Type below: The angle measures are the same Quadrilateral MNPQ has side lengths of 5 mm, 8 mm, 7 mm, and 4 mm. _____________, Answer: Type below: What dilation can you apply to the image to return it to the original preimage? Answer: _____________, Answer: _____________. Which equation does not represent a line with an x-intercept of 3? 325, Algebraic Representations of Dilations Lesson Check Page No. (x, y) -> (1.5x, 1.5y) Question 13. In the given expression, we can notice that the y coordinate is multiplied with 2 Considering the fact that the x coordinate stayed the same and the fact that the y coordinate is multiplied with a number bigger then 1, we can conclude that given figure is vertically streched. b. Page 338: Performance Tasks. Date Class LESSON Algebraic Representations of Dilations Reteach You dilate a figure using the origin as the center of . This standard connects the work done with algebraic functions in grade 8 and Algebra I to geometric functions. _____________, Answer: e. (x, y) (0.5x, 1.5y) Grade: 9, 10, or 11 . Type below: (x, y) -> (1/3x, 1/3y), Question 8. R'(8.75, 2.5), The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals 2. Type below: scale factor = 3, Explanation: (0, 4) (Explore Activities 1 and 2) The drawing has sides measuring 6 cm, 8 cm, and 10 cm, and angles measuring 37, 53, and 90. (9, 6), (3, 6), (9, 3), (3, 3) _____________. Then write them algebraically. _____________, Explanation: B'((3. scale factor of $\frac{1}{3}$ Type below: scale factor = 1/2, Question 19. (x, y) -> (2.5x, 2.5y), Question 3. _____________, Explanation: Question 2. Find the scale factor and the perimeter of each square. _____________, Explanation: For example, if the scale factor is k, the algebraic representation of the dilation is Answer: Miultiply each coordinate of the vertices of ABC by 3 to find the vertices of the dilated image. _____________, Answer: Answer: 90 clockwise rotation, Question 12. Perimeter = ________ units For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates. e. (x, y) (0.5x, 1.5y) What is the effect of a negative scale factor? Displaying all worksheets related to - Algebraic Representations Of Dilations. 2a + a = 8 + 7 Image perimeter: _________, Answer: (x, y) -> (x, -y) The figure is dilated by a factor of 2, but the orientation of the figure in the coordinate plane is rotated 180, Question 1. Critical Thinking MNOP has vertices at M(3, 4), N(6, 4), O(6, 7), and P(3, 7). Thus, the dilation has no effects on the measures of the angles of the image. (x, y) -> (-x, y), Question 11. (-4, 2) Q'(2.5, 2.5), 8th grade. MNPQ is not a dilation of MNPQ, Explanation: Answer: Type below: ________ inches scale factor of $\frac{1}{3}$ -4/-2 =2; 4/2 = 2 Answer: Since the center of dilation is (0, 0), you can simply divide all . _____________, Answer: For 711, tell whether one figure is a dilation of the other or not. (-4, 2) MN = 3, Now, let us determine the value of k, that is -a + 7 = 2a 8 -6/-3 =2; 6/3 = 2 When k is greater than 1, the dilation is an enlargement by the scale factor k. Question 5. (5, -3), Question 5. scale factor = 1/2, Question 19. Your service title Give us a brief description of the service that you are promoting. _____________. _____________, Answer: 324, Algebraic Representations of Dilations Page No. y = 3x 1 (x, y) (y, -x) Type below: letter of the transformation applied. When k is between 0 and 1, the dilation is a reduction by the scale factor k. b. 18/4 = 4.5 mm 15/5 = 3 mm _____________, Explanation: 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: 3x = 1 _____________, Answer: The blueprints are plotted on a coordinate plane. In this lesson, you will learn multiples of 11. (0, 1) Dilation is a process of changing the size of an object while the object remains in the same Shape. A(-5, -4) A'(3 (-5), 3 (-4)) A'(-15, -12) (1) _____________, Answer: No; the dilation is not the same reversed, Explanation: Write the algebraic representation of the dilation shown. How does the dilation affect the length of line segments? June 5, 2022 Posted by: Category: Uncategorized Critical Thinking Explain how you can find the center of dilation of a triangle and its dilation. 8th Grade Texas Mathematics: Unpacked Content 5. For scale factors between 0 and 1, the image is smaller than the preimage.