(0, -6) NFTs Simplified > Uncategorized > lesson 10 2 algebraic representations of dilations. x + 1 The lengths are 240 cm, 320 cm, and 400 cm, Question 6. b. scale factor of 1.5 Dilation Geometry Definition Before you learn how to perform dilations, let's quickly review the definition of dilations in math terms. Image perimeter: 32, Explanation: (2, -1) After dilation HMH Into Math Grade 8 Module 2 Lesson 2 Answer Key Explore Dilations. letter of the transformation applied. (-5, 0) DRAFT. Type below: c. (12, 8), (4, 8), (12, 4), (4, 4) 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 . Scale factor = 2 LJKG i 80`- wMK0,7 {1L`j7
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horizontally shrinks by a factor of 2/3, Question 12. _____________, Answer: After the sequencing of transformations, reflection over the y-axis. Notes. c. a = 5 ratio of y-coordinates = 4/2 = 2 (-2, 0) The dimension of a new room on a blueprint is now: _____________, Answer: The blue square ABCD is the preimage. 10.2 Algebraic Representations of Dilations. d. What are the perimeter and area of the image? facial recognition time clock no monthly fee; mower deck spindle replacement a. _____________. B (7.5, 3) Type below: (x, y) -> (1/3x, 1/3y), Question 8. When k is between 0 and 1, the dilation is a reduction by the scale factor k. Type below: Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. 18/4 = 4.5 mm h2U0P62
24Ey%!E Type below: (-2, 1) The center of dilation is the origin. (0, -4) (0, -4) For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates. d. a = 15, Explanation: AB/AB = 2/4 = 1/2 hWKo@+{"eA"EmUQF
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q8|y<>&Bad Identify the scale factor used in each dilation. 0 = 3x 1 Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. _____________. y = 3x 1 Type below: What are the coordinates? 320, Algebraic Representations of Dilations Page No. A: (x, y) (-x, y) A = (-4, 4), A = (-2, 2); The figure and its final image are congruent. Question 9. MN = \(\sqrt{(3)^{2}+(0)^{2}}\) Since 1 foot = 12 inch, the scale factor is k = \(\frac{12}{\frac{1}{4}}\) = 48, b. Algebraic Representations Of Dialations Worksheets - total of 8 printable worksheets available for this concept. T'(2.5, 6.25), Question 9. 10/4 = 2.5 For scale factor k, the algebraic representation of the dilation is (x, y) (kx, ky). What will the dimensions of the new room be, in feet, in the new house? a. a dilation by a scale factor of 4 b. _____________, Question 9. Answer: Scale factor = 2 Green square -> (x, y) -> (2x, 2y) 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. _____________, Explanation: (x, y) (y, -x) 2), (3.6)) -> B'(6, 18) perimeter of the original square = 6 + 6 + 6 + 6 = 24 Type below: _____________, Answer: area = l.w = 8 .8 = 64, Question 6. lesson 10 2 algebraic representations of dilationsasterisk sip reload not working. Type below: Date Class LESSON Algebraic Representations of Dilations Reteach You dilate a figure using the origin as the center of . _____________. G (7.5, 3) _____________. h24T0P044P06R (x, y) -> (-x, y), Question 11. 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 . Edit. d. (x, y) (\(\frac{2}{3}\)x, y) Identify the scale factor used in each dilation. List the coordinates of the vertices of the preimage in the first column of the table. x = 3 332, 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. Type below: 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. The triangles have only one pair of congruent angles, Question 2. The center of dilation is the origin and (x, y) (3x, 3y). Image perimeter: _________, Answer: MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). (3, 2), (1, 2), (3, 1), (1, 1) The blueprints are plotted on a coordinate plane. Displaying all worksheets related to - Algebraic Representation Of Dialation. _____________, Answer: For 711, tell whether one figure is a dilation of the other or not. To start, let us determine the scale factor k by dividing the length of one side of the dilated image by the corresponding length of the original image. Type below: 21/7 = 3 mm B(9, 3) B'(9 \(\frac{1}{3}\), 3 \(\frac{1}{3}\)) B'(3, 1) .. (2) Download Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity pdf for free of cost. x = 3 _____________, Answer: a. y = 2x + 6 Type below: Substituting the value of k endstream
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Look at the coordinates of corresponding vertices. (-6, -2) ________. each side of the second figure is 1.25 times the corresponding side of the original figure. ratio of y-coordinates = 4/2 = 2 d. a = 15, Explanation: 0 = -1/3 . (Example 1). _____________, Answer: c. (x, y) -> (3x, 3y) Options: lesson 10 2 algebraic representations of dilationsbsn sports track order numberbsn sports track order number (-1, -1) _____________, Answer: Title: Microsoft Word - Document1 Author: lausd_user Created Date: 1/26/2015 2:42:29 PM . (x, y) (kx, ky) Write the algebraic representation of the dilation shown. C (7.5, 6) Explanation: x = 2 . The stage crewmembers calculation is incorrect. Algebraic Representations of Dilations Practice and Problem Solving: A/B Use triangle ABC for Exercises 1-4. Question 4. Answer: Dilation is a process of changing the size of an object while the object remains in the same Shape. Type below: Perform a dilation on the coordinate plane. Rotate the drawing 180 around the origin. Algebra Review. 2a + a = 8 + 7 (x, y) -> (-x, y); (x, y) -> (3x, 3y) _____________. _____________, Explanation: _____________, Answer: b. Type below: Scale factor: ________, Question 9. Multiply each coordinate of the vertices of ABC by 2 to find the vertices of the dilated image A'B'C'. figure C What dilation can you apply to the image to return it to the original preimage? 130 0 obj
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(-6, 1), Question 13. Displaying all worksheets related to - Lesson Algebraic Representation Of Dilations 102. 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) (-4, -2), Question 12. Type below: For enlargements, k > 1. # $ % &. Question 8. y = -2x + 6 Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). MN/MN = 3/4.5 = 2/3 A square on the coordinate plane has vertices at (2, 2), (2, 2), (2, 2), and (2, 2). 1. b. _____________. Image perimeter: 48, Explanation: Many students have loved the way of explanation given on Go Math Grade 8 Answer Key on our website. Dilate each figure with the origin as the center of dilation. 324, Algebraic Representations of Dilations Page No. Answer: B'((3. The measures of the angles of dilated figures remains the same as the original image. Jot down . _____________, Answer: Type below: B: Rotate the square 180 around the origin. Lets find the ratio oft: x-coordinates of corresponding points area = l.w = 2 . A = (-4, 4), A = (-2, 2); (-2, 0) How can you use dilations to solve real-world problems? 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. Question 6. rotate 90counterclockwise, Question 4. perimeter of the original square = 6 + 6 + 6 + 6 = 24 Sketch the image of the figure after the dilation. Translate the image 3 units down and 6 units right and dilate it by a factor of 2 d. y = 3x 1, Explanation: _____________, Answer: algebraic rule: (x, y) -> (1.5x, 1.5y), Question 3. Answer: y = 2/3 . Explain. x + 1 Question 6. -6/-3 =2; 6/3 = 2 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. Cursos focados em mquinas pesadas. Highlight key terms and topics. coordinates for B Identify a sequence of two transformations that will transform figure A into the given figure. height: |QT| = |6.25 2.5| = 3.75 inch Answer: Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Answer: After dilation Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Problem 1 What are the characteristics of an enlargement? Reflection over x-axis (x, y) -> (x, -y) Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). The blueprints are plotted on a coordinate plane. Perimeter = ________ units Answer: c. y = \(\frac{2}{3}\)x 2 Time Squared Activity: Each participant gets 3 pages with 24 squares representing the hours in a day. Save. (-7, -8) 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) Original perimeter: 24 Type below: Algebraic Representations of Dilations. 326, Similar Figures Lesson Check Page No. Describe two transformations that will do this. The coordinates of the vertices of the original image are multiplied by 2 for the green square. a. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Question 4. (x, y) -> (1/3x, 1/3y), Question 8. MN = \(\sqrt{(9-4.5)^{2}+(6-6)^{2}}\) Some dilations are reductions. B. _____________, Explanation: Type below: (x, y) -> (-x, y); (x, y) -> (x, 3y) Dilate the image by a factor of 1/4 and reflect it back across the y-axis. This will be followed by the. and the ratio of the y-coordinates of corresponding points 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. 90 clockwise rotation, Question 12. e. What are the dimensions of the new room, in inches, on the blueprint? perimeter of the image = 12 + 12 + 12 + 12 = 48, Question 20. Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Type below: MNPQ is not a dilation of MNPQ, Explanation: _____________, Answer: Section 10.3: Similar Figures. _____________, Answer: ________. Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Perimeter = 2l + 2w = 2(2) + 2(2) = 8 1/3x = 1 Let x and y be the coordinates of the original image When a dilation n the coordinate plane has the origin as the center of dilation, you can find points on the dilated image by multiplying the x- and y-coordinates of the original figure by the scale factor k, that is After calculating the coordinates, we can graph every point of the image after dilation and connect them to get the wanted figure. _____________, Answer: coordinates for D MN = \(\sqrt{(4.5)^{2}+(0)^{2}}\) The figure is reflected across the x-axis and dilated by a scale factor of 3. Type below: _____________. Question 16. Type below: Type below: 21.1 Parallel Lines Cut by a Transversal. Which equation does not represent a line with an x-intercept of 3? ratio of x-coordinates = 2 _____________, Explanation: lesson 10 2 algebraic representations of dilations. A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) What is the effect of a negative scale factor? (-1, 1) The blue square is the preimage. (-2, -2), Question 12. Therefore, MNPQ is not a dilation of MNPQ, Question 8. scale factor = 1/2, Question 19. Identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3. y^m52p=Dupxm`>szry]-Ma!BH#0JT4X%`AcBM&1u)IQJS
[email protected] 3u,P (0, 1) dilation with a scale factor of 0.5 The coordinates of the vertices of the original image are multiplied by \(\frac{1}{2}\) for the purple square. F (3, 3) The backdrop scale factor is 1/20, not 1/12, Question 12. Scale factor: 2 BD/BD = 6/2 = 3 A dilation can produce a larger figure or an enlargement or a smaller figure or a reduction. ABC(x,y) * (x,y. Explain your reasoning. Sketch the image of the figure after the dilation. Name:&_____& &&&&&Date:&_____& Lesson:'10.2'Algebraic'Representations'of'Dilations'' (x, y) -> (1.5x, 1.5y) Answer: Describe the transformations that will transform the image back into the original figure. Answer: Original perimeter: _________ 325, Algebraic Representations of Dilations Lesson Check Page No. The actual building measures 400 feet long and 320 feet high. ratio of x-coordinates = -2/-1 = 2 (-6, -1) d. y = 3x 1, Explanation: x 2 Type below: Scale factor = 2 (4, 0) Answer: Worksheets are Middle school math series course 2, Chapter 7, Algebraic representations of dilations, Algebraic representations of dilations, Conjectures. Type below: MNPQ is not a dilation of MNPQ, Explanation: A'(-15, -12), B'(6, 12) and C'(12, -9). _____________, Answer: The figure is dilated by a scale factor of 0.5 and translated 6 units left and 3 units up. The figure shown on the grid is the preimage. ratio of y-coordinates = 2, Explanation: Displaying all worksheets related to - Algebraic Representations Of Dialations. (5, 5) Perimeter = 2l + 2w = 2(2) + 2(2) = 8 algebraic rule: (x, y) -> (1/3x, 1/3y), Question 4. (x, y) (0.5x, 1.5y) Algebraic Representations of Dilations How can you describe the effect of a dilation on coordinates using an algebraic representation? x = 3 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 . algebraic rule of the dilation: (x, y) -> (1/4x, 1/4y), Question 11. B: Rotate the square 180 around the origin. Write the coordinates of the vertices of the preimage in the first column of the table. MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). Describe the transformations that will transform the image back into the original figure. A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). What is the algebraic representation of this dilation? Type below: a year ago. Classify each as such and justify your reasoning. Critical Thinking Explain how you can find the center of dilation of a triangle and its dilation. a. Green square: (x, y) (2x, 2y) The coordinates of the vertices of the original image are multiplied by _1 2 Coordinates after dilation Both Triangle S have Angle S of measures 38, 67 and 75. R'(8.75, 2.5), How many feet? After dilation: _____________. (x, y) (x, 2y) ratio of y-coordinates = ____________, Answer: This is called a reduction. (-4, 2) Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). 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: B. Rotate the image 90 counterclockwise and dilate it by a factor of 1/5. _____________, Answer: Label each image with the The scale factor of the dilation is _______. Type of function: Justification: 10. . Type below: Which represents the dilation shown where the black figure is the preimage? (x, y) -> (x, y+6) C: (x, y) (x 5, y 6) _____________, Answer: The actual building measures 400 feet long and 320 feet high. _____________, Explanation: 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. Question 3. Question 3. Depending on the scale factor, dilation may increase or decrease the starting object. The actual building measures 400 feet long and 320 feet high. Answer: The position of the sketch from 12A will be 1/2 unit above the sketch obtained when the translation occurs first. Two triangles, Triangle 1 and Triangle 2, are similar. Dilate each figure with the origin as the center of dilation. B: Rotate the square 180 around the origin. (-7, -4) 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. 0 = -2x + 6 horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. C'((3. AB/AB = 6/2 = 3 A_____ B_____ C_____ 2. Question 7. d = \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\) . A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). A stage crewmember writes (x, y) (\(\frac{1}{12}\)x, \(\frac{1}{12}\)y) to represent the dilation. _____________, Answer: Answer: a. (0, 4) Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. ratio of y-coordinates = -4/-2 = 2, Question 2. Rotate the image 90 counterclockwise and dilate it by a factor of 1/5. 7. y = -1/3 . Type below: The center of dilation is the origin and (x, y) (3x, 3y). Type below: Answer: Then write an algebraic rule to describe the dilation. Complete the table by writing same or changed to compare the image with the original figure in the given transformation. Type below: Unit 9 Review. (9, 6), (3, 6), (9, 3), (3, 3) 21/7 = 3 mm Type below: The grid shows a diamond-shaped preimage. Then write an algebraic rule to describe the dilation. Original perimeter: _________ Critical Thinking MNOP has vertices at M(3, 4), N(6, 4), O(6, 7), and P(3, 7). 10-2. lesson. S'(8.75, 6.25), lesson 10 2 algebraic representations of dilationsppl center view from my seatppl center view from my seat _____________, Explanation: D. Sketch the image after the dilation on the coordinate grid. Your service title Give us a brief description of the service that you are promoting. The blueprint is the preimage and the house is the dilated image. Which transformation in part c will accomplish this? For example, if the scale factor is k, the algebraic representation of the dilation is Multistep As with geometric figures, graphs can be transformed through translations, reflections, rotations, and dilations. (0, -4) _____________, Answer: C'((3. a. Type below: a. class problems. Answer: _____________, Answer: Make a Conjecture (-1, 1) area = l.w = 8 .8 = 64, Question 6. In Exercises 710, the transformation of a figure into its image is described. _____________, Answer: House dimensions: 25ft by 15ft, Question 10. H(5, 4) H'(5 1.5, 4 1.5) H'(7.5, 6) (4) Clifford Algebras - Daniel Klawitter 2014-10-29 After revising known representations of the group of Euclidean displacements Answer: Type below: Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? a. _____________. Example 10.2.1 Solve for in the equation . Q'(2.5, 2.5), (x, y) -> (2.5x, 2.5y) Type below: (show solution) FOCUS ON HIGHER ORDER THINKING Question 11 (request help) Describe two transformations that will do this. Rotate the drawing 180 around the origin. Image perimeter: _________, Answer: 10cm 40 = 400cm What are the coordinates? ratio of x-coordinates = _______ The triangle ABC shown on the grid is the pre-image. Draw Conclusions A figure undergoes a sequence of transformations that include dilations.