To create the actual sign shown, the drawing must be dilated using a scale factor of 40. x 2 area = l.w = 2 . ________. T'(2.5, 6.25), Question 9. Rotate the image 90 counterclockwise and dilate it by a factor of 1/5. Perimeter = ________ units (x, y) -> (1.5x, 1.5y) B (7.5, 3) 10.2 Independent Practice - Algebraic Representations of Dilations - Page No. Type below: For example, if the scale factor is k, the algebraic representation of the dilation is F (3, 3) Type below: Type below: _____________, Answer: What is the scale factor in terms of inches to inches? Identify the scale factor used in each dilation. 320, Algebraic Representations of Dilations Page No. The square is dilated under the dilation (x, y) (0.25x, 0.25y). The HMH Go Math 8th Grade Chapter 10 Transformations and Similarity Solution Key includes properties of dilations, Algebraic Representations of Dilations, and similar figures. Multiply each coordinate of the vertices of ABC by 2 to find the vertices of the dilated image A'B'C'. c. Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image. endstream endobj 134 0 obj <>stream meaning that we will multiply every coordinate with \(\frac{3}{2}\). c. (x, y) -> (x, -y); (x, y) -> (3x, y) algebraic rule: (x, y) -> (1/3x, 1/3y), Question 4. Answer: Answer: A(8, 0) A' . Triangle XYZ has angles measuring 54 and 29. The homeowner wants this room to be 25% larger. d = \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\) area = l.w = 8 .8 = 64, Question 6. _____________. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 13.2 Answer Key Algebraic Representations of Dilations. 37, 53, and 90, Question 6. e. (x, y) (0.5x, 1.5y) (9, 6), (3, 6), (9, 3), (3, 3) (Explore Activities 1 and 2) perimeter of the image = 12 + 12 + 12 + 12 = 48, Question 20. 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 _______. _____________, Answer: _____________, Answer: _____________, Answer: _____________, Answer: Grade: 9, 10, or 11 . Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. 3/2 (0, -4) (x, y) -> (2.5x, 2.5y), Question 3. The vertices of the dilated image are A'(1, 1), B'(3, 1), and C'(1, 3). _____________, Explanation: a dilation produces an image similar to the original figure, Question 10. MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). Type below: (x, y) -> (1/3x, 1/3y), Question 8. Type below: Determine whether one figure is a dilation of the other. Original perimeter: _________ Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). 325, Algebraic Representations of Dilations Lesson Check Page No. After dilation Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. endstream endobj 131 0 obj <>stream Algebraic Representations of Dilations. I (3, 6) The sides are proportional. What are the vertices of the dilated image? Yes; Quadrilateral DEFG is a dilation of quadrilateral DEFG. (x, y) -> (x, -y) d. (x, y) (\(\frac{2}{3}\)x, y) 10/4 = 2.5 AB/AB = 2/4 = 1/2 Displaying all worksheets related to - Algebraic Representations Of Dialations. Graph the image of each figure after a dilation with the origin as its center and the given scale factor. C'(12, -9), Explanation: c. a reflection across the y-axis (2x, 2y) 5. 2x = 6 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. For scale factors between 0 and 1, the image is smaller than the preimage. _____________, Answer: 8th Grade Texas Mathematics: Unpacked Content 5. Explain. 324, Algebraic Representations of Dilations Page No. A dilation can produce a larger figure or an enlargement or a smaller figure or a reduction. C: (x, y) (x 5, y 6) Make a Conjecture After dilation: (Example 1). b. Section 10.3: Similar Figures. Options: Answer: Make a Conjecture Participants need to fill out: The first page . )X}Dh=64z!vv 8 Some dilations are enlargements. 10cm 40 = 400cm Question 1. relay for life dates 2022. (x, y) -> (1/3x, 1/3y), Question 8. Which represents the dilation shown where the black figure is the preimage? (x, y) -> (-x, y); (x, y) -> (3x, 3y) (-4, 4) The figure is dilated by a factor of 2, but the orientation of the figure in the coordinate plane is rotated 180, Question 1. Examples, solutions, videos, worksheets, games, and activities to help geometry students learn. c. a = 5 ratio of x-coordinates = -4/-2 = 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. Quadrilateral MNPQ has side lengths of 15 mm, 24 mm, 21 mm, and 18 mm. Answer: 10.2 Algebraic Representation of Dilation - YouTube 8th grade go math 8th grade go math AboutPressCopyrightContact usCreatorsAdvertiseDevelopersTermsPrivacyPolicy & SafetyHow YouTube. Explain your reasoning. 2a + a = 8 + 7 The grid shows a diamond-shaped preimage. A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). 10/4 = 2.5 Options: What is the effect on the figure when k > 1? _____________, Question 9. Describe two transformations that will do this. Image perimeter: 32, Explanation: 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 After dilation Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. MNOP has vertices at M(4.5, 6), N(9, 6), O'(9, 10.5), and P'(4.5, 10.5). 715 Module 20 Lesson 2 Algebraic Representation of Dilation DRAFT. MN/MN = 3/4.5 = 2/3 List the coordinates of the vertices of the preimage in the first column of the table. (-2, 2) BD/BD = 6/2 = 3 Q'(2.5, 2.5), Image perimeter: 48, Explanation: The figure is reflected across the y-axis and dilated by a scale factor of 4. Type below: Options: Triangle RST has angles measuring 38 and 75. (0, -4) A: (x, y) (-x, y) The coordinates of the vertices of the original image are multiplied by 2 for the green square. 13.2. C (7.5, 6) _____________. Type below: The corresponding angles of triangle ABC and triangle ABC are congruent. Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. Type below: 2 = 4. (-4, 2) Sketch the image of the figure after the dilation. Answer: class problems. _____________, Answer: Answer: ratio of x-coordinates = _______ (0, 4) Type below: The Go Math Grade 8 Solution Key Chapter 10 Transformations and Similarity help the students to enhance their math skills. _____________. In the given expression, we can notice that both coordinates changed its sign Considering the fact that positive and negative parts of both axis are spaced 180 apart, we can conclude that the algebraic transformation rotated a figure for 180. (0, -4) Notes. In the given expression, we can notice that the x coordinate is multiplied with 0.5 and that the y-coordinate is multiplied with 1.5. Explain. Question 4. Complete the table by writing same or changed to compare the image with the original figure in the given transformation. For 711, tell whether one figure is a dilation of the other or not. figure B A crewmember wrote wrong, the dilation is (x, y) (\(\frac{1}{20}\)x, \(\frac{1}{20}\)y). Question 7. The figure is dilated by a factor of 2, but the orientation of the figure in the coordinate plane is rotated 180, Question 1. Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. _____________, Explanation: 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! Answer: e. What are the dimensions of the new room, in inches, on the blueprint? The center of dilation is the origin. (0, 4) Page 337: Study Guide Review: Module 10. What is the scale factor for the dilation? Length of MN, given M(4.5, 6), N(9, 6). cfelg. Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. (0, -3) c. a = 5 a year ago. Answer: Type below: 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 . Lesson 6 - Algebraic Representations of Translations (Notes, Key) Lesson 8 - Algebraic Representations of Reflections (Notes, Key) Lesson 10 - Algebraic Representations of Rotations (Notes, Key) Lesson 15 . Type below: Answer: _____________, Answer: (5, -3), Question 5. Perimeter = 2l + 2w = 2(2) + 2(2) = 8 Triangle XYZ has angles measuring 54 and 29. The blue square is the preimage. What dilation can you apply to the image to return it to the original preimage? _____________, Explanation: Question 6. _____________. (1, 1) For enlargements, k > 1. (-1, -1) Mod 20-2 Class Problems. Q'(2.5, 2.5), In Exercises 710, the transformation of a figure into its image is described. C'(12, -9), Explanation: (x, y) (-x, -y) Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? Write the algebraic representation of the dilation shown. h2W0P+-60rb X;; | ________. Identify a sequence of two transformations that will transform figure A into the given figure. Explain how this can happen. Answer: Multiply each coordinate of the vertices of rectangle FGHI by 1, 5 to find the vertices of the dilated image. Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Save. Identify a sequence of two transformations that will transform figure A into the given figure. a. a dilation by a scale factor of 4 (-2, -2), Question 12. C(3, 9) C'(3 \(\frac{1}{3}\), 9 \(\frac{1}{3}\)) C'(1, 3) (3) Answer: ______ units, Question 6. Question 6. Write the coordinates of the vertices of the preimage in the first column of the table. DRAFT. Type below: 0 = 3x 1 (-6, 1), Question 13. Algebraic Representation Calculus Absolute Maxima and Minima Absolute and Conditional Convergence Accumulation Function Accumulation Problems Algebraic Functions Alternating Series Antiderivatives Application of Derivatives Approximating Areas Arc Length of a Curve Area Between Two Curves Arithmetic Series Average Value of a Function