House dimensions: 25ft by 15ft, Question 10. _____________, Answer: 10.2 Algebraic Representations of Dilations. Participants need to fill out: The first page . Notes. Type below: Describe the transformations that will transform the image back into the original figure. The scale factor is the number that describes the change in size in a dilation Make sure that students bubble in their answers for the front page (#1-7) and the back page (#8-14). _____________, Answer: (-2, 0) a = 5, Question 5. (x, y) -> (1.5x, 1.5y) Thus, the dilation has no effects on the measures of the angles of the image. d. a = 15, Explanation: Critical Thinking A dilation with center (0, 0) and scale factor k is applied to a polygon. Type below: B(9, 3) B'(9 \(\frac{1}{3}\), 3 \(\frac{1}{3}\)) B'(3, 1) .. (2) 5/2 = 2.5 Triangle UVW has coordinates U(15, 9), V(6, 4.5), and W(18, -3). A (3, 3) (-2, -2), Question 12. _____________, Answer: After dilation: (1, -1) Image perimeter: _________, Answer: Question 5. Answer: 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. How does the dilation affect the length of line segments? community surgical supply lawsuit; . MN = \(\sqrt{(4.5)^{2}+(0)^{2}}\) The center of dilation is the origin and (x, y) (3x, 3y). _____________. dilation with a scale factor of 0.5 Type below: (show solution) FOCUS ON HIGHER ORDER THINKING Question 11 (request help) A rectangle has vertices (6, 4), (2, 4), (6, 2), and (2, 2). _____________, Answer: (2, 2) What will the dimensions of the new room be, in feet, in the new house? Explain. -4/-2 =2; 4/2 = 2 62 3099-5574 R. Quintino Bocaiva, 359, Centro - Anpolis/GO . Write the coordinates of some of the points on first graph: A(-2, 4), B(2, 4), C(0, -4), and on second graph: _____________. Coordinates after dilation (-4, 4) Describe how the graph of y = x shown at the right is changed through each of the following transformations. B = (4, 2), B = (2, 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. 3x = 1 coordinates for B (x, y) -> (1/5x, 1/5y), Question 10. (x, y) -> (2.5x, 2.5y) Multiple Choice Use the diagram below to find the value of x. . Multiply each coordinate of the vertices of ABC by 3 to find the vertices of the dilated image. MN = \(\sqrt{(3)^{2}+(0)^{2}}\) (-5, 0) Blueprint dimensions: 6.25 in. Type below: One inch on the blueprint represents 1 48 feet = 48 \(\frac{1}{12}\) inch = 4 inch, c. Write the algebraic representation of the dilation from the blueprint to the house. 2), (3.6)) -> B'(6, 18) Type below: c. Write the algebraic representation of the dilation from the blueprint to the house. _____________, Answer: How many feet? After dilation After dilation Dilate the triangle with vertices of (2, 2), (4, 6), and (6, 2); a scale factor of 1/2, with the origin as the center of dilation. C = (-2, -4), C = (-1, -2); The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals 2. 37, 53, and 90, Question 6. Question 7. Quadrilateral MNPQ is the same shape but a different size than quadrilateral MNPQ. Type below: Scale factor: ________, Question 9. 326, Similar Figures Lesson Check Page No. One inch on the blueprint represents how many inches in the actual house? Represent Real-World Problems The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. Question 4. What are the vertices of the dilated image? Answer: What is the length of a side of the image? _____________, Answer: No; one figure is not a dilation of the other, Explanation: perimeter of the original square = 4 + 4 + 4 + 4 = 16 A(8, 0) A' . (x, y) -> (-x, y); (x, y) -> (x, 3y) a. (x, y) -> (x, -y) Answer: Question 9. _____________, Explanation: The vertices of the dilated image are F'(3.5, 3.5), G'(7.5, 3.5), H'(7.5, 6) and I'(, 9). Type of function: Justification: 9. = 3 2 + 3. One inch on the blueprint represents how many inches in the actual house? (7, 8) 2/3x = 2 When k is between 0 and 1, the dilation is a reduction by the scale factor k. horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. _____________, Explanation: Total Meals Sent Learn More. 324, Algebraic Representations of Dilations Page No. Displaying all worksheets related to - Lesson Algebraic Representation Of Dilations 102. B(-2, 1) B'( 2 ( 2), 2 1) B'(4, -2) .. (2) (5, -3), Question 5. Lesson 2: Algebraic Representations of Dilations, Question 1. Multiply each coordinate of the vertices of triangle ABC by \(\frac{1}{3}\) to find the vertices of the dilated image. The algebric dilation is (x, y) (48x, 48y). Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. 0 = -1/3 . 77% average accuracy. _____________, Answer: 0 = -2x + 6 figure C class problems. e. (x, y) (0.5x, 1.5y) What is the algebraic representation of this dilation? A: (x, y) (-x, y) The perimeter of the image is the perimeter of the original figure times the scale factor, Question 1. coordinates for D 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! relay for life dates 2022. House dimensions: 25ft by 15ft, Question 10. Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. 6cm 40 = 240cm (x, y) -> (2.5x, 2.5y), Question 3. Perimeter = ________ units _____________, Answer: 10.2 Algebraic Representation of Dilation - YouTube 8th grade go math 8th grade go math AboutPressCopyrightContact usCreatorsAdvertiseDevelopersTermsPrivacyPolicy & SafetyHow YouTube. No; one figure is not a dilation of the other, Explanation: _____________, Answer: d. (x, y) -> (6x, 6y), Explanation: d. (x, y) (\(\frac{2}{3}\)x, y) (x, y) ( x, -y) _____________, Answer: examples of gram negative spore forming bacteria. c. a = 5 Perimeter = 2l + 2w = 2(2) + 2(2) = 8 c. The drawing has the hypotenuse on the bottom. Type below: D: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y) 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. MN = \(\sqrt{20.25}\) vertically stretches by a factor of 2, Question 12. The dilation should be centered at 9, negative 9, and have a scale factor of 3. ratio of y-coordinates = -4/-2 = 2, Question 2. Explain how this can happen. 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. (x, y) -> (-x, y); (x, y) -> (3x, 3y) Perimeter = 2l + 2w = 2(2) + 2(2) = 8 What are the coordinates of the new room? _____________, Explanation: _____________, Answer: _____________, Explanation: The first one is done for you. The business owner would like it on the top. Edit. _____________, Explanation: 18/4 = 4.5 mm Quadrilateral MNPQ has side lengths of 5 mm, 8 mm, 7 mm, and 4 mm. Multiply each coordinate by the scale . The scale factor of the dilation is _______. rotate 90counterclockwise, Question 4. Type below: _____________, Answer: The actual building measures 400 feet long and 320 feet high. Type below: Answer: LJKG i 80`- wMK0,7 {1L`j7 Fi@W_w ~H; po0]uWuvGG]nB\9LgxG:1~}_ G lesson 10 2 algebraic representations of dilationsasterisk sip reload not working. Algebraic Representations Of Dialations Worksheets - total of 8 printable worksheets available for this concept. Scale factor: _________ (-3, -4) Area = ________ square units, Answer: Options: Scale factor: ________, Question 9. MNPQ is not a dilation of MNPQ, 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? 4. e. (x, y) (0.5x, 1.5y) Substituting the value of k B: Rotate the square 180 around the origin. After the sequencing of transformations, reflection over the y-axis. (-1, 1) (-1, -1), Question 6. Type below: The drawing has sides measuring 6 cm, 8 cm, and 10 cm, and angles measuring 37, 53, and 90. 23 times. (2, 2) Scale factor: _________ (Explore Activities 1 and 2) d. a = 15, Explanation: 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. 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. Blueprint dimensions: 6.25 in. 13.2. Highlight key terms and topics. I can describe what happens when two-dimensional figures are transformed using coordinates. 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. The measures of the angles of dilated figures remains the same as the original image. Justify Reasoning The graph of the line y = x is dilated by a scale factor of 3 and then translated up 5 units. algebraic rule: (x, y) -> (2/3x, 2/3y), Question 8. Type below: Translate the image 3 units down and 6 units right and dilate it by a factor of 2 figure C Perimeter = 32 units Multistep As with geometric figures, graphs can be transformed through translations, reflections, rotations, and dilations. Question 3. AB/AB = 6/2 = 3 x 2 Rotate the drawing 180 around the origin. (-5, 0) 0 = 3x 1 146 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 . If two figures are similar but not congruent, what do you know about the sequence of transformations used to create one from the other? Therefore, MNPQ is not a dilation of MNPQ, Question 8. A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). Scale factor: 2 So, the scale factor is \(\frac{1}{20}\), and algebric rule of dilation is (x, y) (\(\frac{1}{20}\)x, \(\frac{1}{20}\)y) A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). (x, y) (x, 2y) coordinates for C Texas Go Math Grade 8 Lesson 13.2 Explore Activity Answer Key. _____________. Type below: Filled table is shown in the picture below. Describe the image of a dilation with a scale factor of 1. Then write an algebraic rule to describe the dilation. Then write them algebraically. b. 0 = 2/3 . x + 1 Quadrilateral MNPQ is the same shape but a different size than quadrilateral MNPQ. 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. (x, y) (\(\frac{2}{3}\)x, \(\frac{2}{3}\)y). Type below: What is the algebraic representation of this dilation? Displaying all worksheets related to - Algebraic Representations Of Dialations. h2U0P62 24Ey%!E Type below: 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 . Type below: _____________, Answer: How does the dilation affect angle measures? y = 3x 1 Type below: Students use algebraic representations of dilations worksheet is a grid units. Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Explanation: \(\frac{-\frac{1}{2}}{-2}=\frac{\frac{1}{2}}{2}=\frac{1}{4}\) No; the dilation is not the same reversed, Explanation: Which transformation in part c will accomplish this? (x, y) (y, -x) Make a Conjecture Algebraic Representations of Dilations You dilate a figure using the origin as the center of dilation. coordinates for D each side of the second figure is 1.25 times the corresponding side of the original figure. So, to learn maths in the best way, you must refer to HMH Go Math Grade 8 Solution Key. (0, -6) The corresponding angles of triangle ABC and triangle ABC are _______. What is the effect on the figure when k > 1? The blueprints are plotted on a coordinate plane. (1, 1) Options: 326, Similar Figures Lesson Check Page No. (x, y) (y, -x) _____________, Answer: On a coordinate plane, triangle UVW has coordinates U(20, 12), V(8, 6), and W(24, -4). Describe how the graph of y = x shown at the right is changed through each of the following transformations. Which transformation in part c will accomplish this? (-7, -8) Answer: G (7.5, 3) Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. y = 2/3 . (x, y) (y, -x) Apply each transformation to the image of the previous transformation. A: (x, y) (-x, y) _____________. The figure and its final image are congruent. Since 1 foot = 12 inch, the scale factor is k = \(\frac{12}{\frac{1}{4}}\) = 48, b. endstream endobj 137 0 obj <>stream a. a dilation by a scale factor of 4 Area = ________ square units, Answer: Answer: and find the ratio of heigh: \(\frac{16}{320}\) = \(\frac{1}{20}\) The position of the sketch from 12A will be 1/2 unit above the sketch obtained when the translation occurs first. Triangle XYZ has angles measuring 54 and 29. 2a + a = 8 + 7 ratio of y-coordinates = 2/1 = 2 d. (x, y) (\(\frac{2}{3}\)x, y) _____________, Answer: _____________, Answer: x = 3 Clifford Algebras - Daniel Klawitter 2014-10-29 After revising known representations of the group of Euclidean displacements What will the dimensions of the new room be, in feet, in the new house? _____________. Scale factor = 2 _____________, Answer: (x, y) -> (-x, y), Question 11. Area = ________ square units, Answer: ratio of y-coordinates = 2/1 = 2 Question 2. Answer: (x, y) -> (1.5x, 1.5y) coordinates for A A'((3.-15), (3.-12)) -> A'(-15, -12) Mod 20-2 Class Problems. The lengths are 240 cm, 320 cm, and 400 cm, Question 6. Look at the coordinates of corresponding vertices. b. Identify a sequence of two transformations that will transform figure A into the given figure. (-2, 0) The homeowner wants this room to be 25% larger. 21/7 = 3 mm Critical Thinking Explain how you can find the center of dilation of a triangle and its dilation. What dilation can you apply to the image to return it to the original preimage? Type below: 10.2 Independent Practice - Algebraic Representations of Dilations - Page No. Answer: _____________, Explanation: F (3, 3) In Exercises 710, the transformation of a figure into its image is described. k = \(\frac{2}{3}\), Next, Let us represent the dilation algebraically, using x 2 translation 2 units left and 2 units up, Question 6. _____________, Answer: A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). After dilation Question 5. Then write an algebraic rule to describe the dilation. Find the scale factor and the perimeter of each square. ratio of y-coordinates = 4/2 = 2 a. scale factor of \(\frac{1}{3}\) MN = \(\sqrt{9}\) _____________, Explanation: horizontally shrinks by a factor of 2/3, Question 12. A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) Page 338: Performance Tasks. B (7.5, 3) (-4, -2) Answer: x = 2 . d. A rectangular room has coordinates Q(2, 2), 6(7, 2), S(7, 5), and T(2, 5) on the blueprint. Question 3. (5, -3), Question 5. So, the scale factor of the dilation is 3/4. _____________, Explanation: Also, get the solutions to the review test on our Go Math Grade 8 Answer Key. Give the coordinates of each vertex of ABC. (-1, -1) b. (5, 5) Q'(2.5, 2.5), ratio of x-coordinates = -4/-2 = 2 B'(6, 18) (-4, 2) After the sequencing of transformations, reflection over the y-axis. endstream endobj 136 0 obj <>stream (-2.5, 2.5) 10 x 10 = 7 x 2 = 10 x 9 = 5 x 8 = 10 x 3 = How did you do? (5, 5) The corresponding angles of triangle ABC and triangle ABC are congruent. You can use dilations when drawing or designing, Question 1. The scale factor of the dilation is 2. The perimeter of the image is the perimeter of the original figure times the scale factor, Question 1. Explanation: )ABC lesson 10 2 algebraic representations of dilationsmercedes financial services phone numbermercedes financial services phone number MN/MN = 3/4.5 = 2/3 Sketch triangle ABC and ABC for the dilation (x, y) (-2x, -2y). T'(2.5, 6.25), Question 9. b. Answer: Dilation is a process of changing the size of an object while the object remains in the same Shape. Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). scale factor = 1/2, Question 19. c. What are the perimeter and area of the preimage? Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. A stage crew member writes (x, y) (\(\frac{1}{12}\)x, \(\frac{1}{12}\)y) to represent the dilation. What is the scale factor in terms of inches to inches? (x, y) (2x, 2y) (x, y) (0.5x, 1.5y) (7, 4) 1/3x = 1 (x, y) (y, -x) (x, y) (\(\frac{2}{3}\)x, y) Type below: MN = \(\sqrt{(9-4.5)^{2}+(6-6)^{2}}\) _____________, Explanation: G7 Math Lesson 10.2 Algebraic Representations of Dilations STUDY Flashcards Learn Write Spell Test PLAY Match Gravity algebraic expression Click card to see definition Click again to see term 1/15 Created by weiennlee TEACHER Terms in this set (15) algebraic expression dilation vertex (plural: vertices) (:vertices) Type below: a. Therefore, considering the fact that the coordinate is multiplied with a number smaller then 1 and the fact that the y coordinate is multiplied with a number bigger then 1, we can conclude that given figure is horizontally shrikned and vertically streched. Coordinates after dilation (4, 0) _____________, Answer: The grid shows a diamond-shaped preimage. (9, 6), (3, 6), (9, 3), (3, 3) Type below: h2S0PP02]KsSJ Tu! Scale factor: _________ What are the coordinates of the new room? (-2, 0) F (3, 3) c. (12, 8), (4, 8), (12, 4), (4, 4) Explanation: The triangles have only one pair of congruent angles, Question 2. a year ago. _____________. (-4, 0), Question 4. _____________, Answer: The image is congruent to the original figure. Edit. _____________. (0, -4) _____________, Answer: When k is between 0 and 1, the dilation is a reduction by the scale factor k. Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. For scale factors between 0 and 1, the image is smaller than the preimage. D: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y) y = -1/3 . For 711, tell whether one figure is a dilation of the other or not. ratio of x-coordinates = 4/2 = 2 Dilation Geometry Definition Before you learn how to perform dilations, let's quickly review the definition of dilations in math terms. 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: The arrow shown is the preimage. Some dilations are enlargements. Explanation: Original perimeter: 16 Type below: 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. Two triangles, Triangle 1 and Triangle 2, are similar. Image perimeter: _________, Answer: A square on the coordinate plane has vertices at (2, 2), (2, 2), (2, 2), and (2, 2). ! " _____________. A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). d. The shorter leg of the drawing is currently on the left. (0, -4) Type below: Triangle RST has angles measuring 67 and 38. Which represents the dilation shown where the black figure is the preimage? Quadrilateral MNPQ has side lengths of 15 mm, 24 mm, 21 mm, and 18 mm. a. 320, Algebraic Representations of Dilations Page No. (2, -2) The backdrop scale factor is 1/20, not 1/12, Question 12. a. a = -3 Represent Real-World Problems The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. horizontally shrinks by a factor of 2/3, Question 12. ABC(x,y) * (x,y. e. What are the dimensions of the new room, in inches, on the blueprint? ________. b. A. 20.2 Algebraic Representations of Dilations. What is the scale factor for the dilation? 4), (3.-3)) -> C'(12, -9), Question 7. Find the angle measures of the actual sign. c. (x, y) (x, 2y) When k is greater than 1, the dilation is an enlargement by the scale factor k. Texas Go Math Grade 8 Lesson 13.2 Independent Practice Answer Key, Question 5. 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 . MN/MN = 3/4.5 = 2/3 The solution for this requires that you take the fifth root of both sides. 10cm 40 = 400cm b. The dimension of a new room on a blueprint is now: The blue square ABCD is the preimage. A dilation of (x, y) (kx, ky) when 0 < k < 1 has what effect on the figure? Translate the image 3 units down and 6 units right and dilate it by a factor of 2 Graph the dilation. Question 7. Explain how this can happen. Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? _____________. Reflection over x-axis (x, y) -> (x, -y) (-4, -2), Question 12. Mod20-2Notes. So, the corresponding S are congruent. Thus Download Go Math Grade 8 Chapter 10 Transformations and Similarity Answer Key PDF and start your practice.
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