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Options: The center of dilation is the origin. 10cm 40 = 400cm Type below: Type below: Describe two transformations that will do this. Highlight key terms and topics. _____________, Answer: (1, -1) Graph the image of each figure after a dilation with the origin as its center and the given scale factor. and the ratio of the y-coordinates of corresponding points _____________, Answer: Area = 64 square units, Explanation: b. a translation down 3 units Yes; Quadrilateral DEFG is a dilation of quadrilateral DEFG. Justify Reasoning The graph of the line y = x is dilated by a scale factor of 3 and then translated up 5 units. dilation by scale factor of 3 (x, y) -> (3x, 3y) (0, -6) d. y = 3x 1, Explanation: 13.2. 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) _____________, Answer: dilation by scale factor of 3 (x, y) -> (3x, 3y) 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: Type below: 10-2. lesson. The center of dilation is the origin. 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 lengths are 240 cm, 320 cm, and 400 cm, Question 6. MNPQ is not a dilation of MNPQ, Explanation: (-1, -1) Learning is not only important but understanding the concepts is also important for the students to enhance their skills. G (7.5, 3) A(0, 8), B(0, 0), C(10, 0) 3. _____________, Question 9. (2x, 2y) 5. C(-2, 4) C'( 2 (- 2), 2 4) C'(4, -8) . y = 2/3 . (4, 0) Question 5. _____________, Answer: Original perimeter: _________ Scale factor: ________, Question 9. _____________, Answer: No; the dilation is not the same reversed, Explanation: What are the coordinates of the new room? The perimeter of the image is the perimeter of the original figure times the scale factor, Question 1. How can you find the scale factor of a dilation? _____________. S'(8.75, 6.25), Type below: Type below: Green square -> (x, y) -> (2x, 2y) So, to learn maths in the best way, you must refer to Go Math Grade 8 Answer Key. The coordinates of the vertices of the original image are multiplied by 2 for the green square. Question 2. The figure is dilated by a factor of 2, but the orientation of the figure in the coordinate plane is rotated 180, Question 1. _____________, Explanation: # $ % &. ________. So, the scale factor of the dilation is 3/4. CorrectionKey=B Transformations and Similarity MODULE 10 3. lesson 10 2 algebraic representations of dilations class problems. Type below: Reflect the drawing over the x-axis a. Question 1. (4, 0) Options: (-4, 4) _____________, Answer: Reflect the drawing over the x-axis Rotate the image 90 counterclockwise and dilate it by a factor of 1/5. Perimeter = 32 units C (7.5, 6) I (3, 6) (-4, -2) Which represents the dilation shown where the black figure is the preimage? Reflection over x-axis (x, y) -> (x, -y) Perimeter = 2l + 2w = 2(2) + 2(2) = 8 ratio of x-coordinates = -4/-2 = 2 What dilation can you apply to the image to return it to the original preimage? )X}Dh=64z!vv 8 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. Section 10.3: Similar Figures. The explanations seen in Go Math Grade 8 Answer Key Chapter 10 are prepared by the concerned subject experts. 21.1 Parallel Lines Cut by a Transversal. 2a + a = 8 + 7 For scale factor k, the algebraic representation of the dilation is (x, y) (kx, ky). Determine the coordinates of its image after a dilation with the given scale factor centered at the origin. b. After calculating the coordinates, we can graph every point of the image after dilation and connect them to get the wanted figure. Answer: The stage crewmembers calculation is incorrect. 15/5 = 3 mm When k is greater than 1, the dilation is an enlargement by the scale factor k. Question 5. _____________, Answer: A square on the coordinate plane has vertices at (2, 2), (2, 2), (2, 2), and (2, 2). Options: Answer: Sketch the image of the figure after the dilation. MN = 3, Now, let us determine the value of k, that is AB/AB = 2/4 = 1/2 b. OL@6BxtiJZ7f)^H(pjl4.I`'Fq rm;`$PE\!0P{a!-;}])o1Y-f /PMM$4x*gv|DeF. |_]prV8!Q~~p Question 3. Both Triangle S have Angle S of measures 38, 67 and 75. Multiply each coordinate of the vertices of triangle ABC by \(\frac{1}{3}\) to find the vertices of the dilated image. 5/2 = 2.5 B'((3. (x, y) -> (-x, y); (x, y) -> (x, 3y) _____________, Explanation: The explanations seen in Go Math Grade 8 Answer Key Chapter 10 are prepared by the concerned subject experts. Clifford Algebras - Daniel Klawitter 2014-10-29 After revising known representations of the group of Euclidean displacements _____________, Answer: Represent Real-World Problems The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. 2 = 4. Type below: lesson 10 2 algebraic representations of dilations; Identify the scale factor used in each dilation. Critical Thinking MNOP has vertices at M(3, 4), N(6, 4), O(6, 7), and P(3, 7). 6cm 40 = 240cm Answer: _____________, Answer: endstream endobj 133 0 obj <>stream c. (x, y) (x, 2y) What are the coordinates? (-6, -1) Type below: scale factor = 1/2, Question 19. Coordinates after dilation _____________, Answer: The business owner would like it on the top. ________ inches ratio of x-coordinates = 4/2 = 2 The drawing has sides measuring 6 cm, 8 cm, and 10 cm, and angles measuring 37, 53, and 90. DRAFT. (-3, -4) Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Describe the image of a dilation with a scale factor of 1. 3a = 15 ratio of x-coordinates = _______ The position of the sketch from 12A will be 1/2 unit above the sketch obtained when the translation occurs first. ratio of y-coordinates = 2/1 = 2 So, the corresponding S are congruent. 21/7 = 3 mm Question 1. (-6, -1) B: Rotate the square 180 around the origin. The coordinates of the vertices of the original image are multiplied by \(\frac{1}{2}\) for the purple square. In feet 6.25 4 = 25ft and 3.75 4 = 15 ft, Question 10. > ~ y o I (3, 6) (9, 6), (3, 6), (9, 3), (3, 3) 10.2 Algebraic Representations of Dilations. (7, 4) x = 1/3, Question 6. _____________, Answer: (-2, -2) 21/7 = 3 mm ________ inches (x, y) (-x, -y) Type below: So, to learn maths in the best way, you must refer to HMH Go Math Grade 8 Solution Key. Go Math Grade 5 Answer Key Pdf | Go Math 5th Grade Answer Key Pdf, McGraw Hill Math Grade 8 Lesson 21.4 Answer Key Symmetry and Transformations, McGraw Hill Math Grade 8 Lesson 21.3 Answer Key Circles, McGraw Hill Math Grade 8 Lesson 21.2 Answer Key Polygons, McGraw Hill Math Grade 8 Lesson 21.1 Answer Key Quadrilaterals, McGraw Hill Math Grade 8 Lesson 20.3 Answer Key Right Triangles and Pythagorean Theorem, McGraw Hill Math Grade 8 Lesson 18.2 Answer Key Line Segments and Rays, McGraw Hill Math Grade 8 Lesson 20.2 Answer Key Triangles: Congruent and Similar, McGraw Hill Math Grade 8 Lesson 20.1 Answer Key Triangles: Acute, Right, Obtuse, Equilateral, Isosceles, and Scalene, McGraw Hill Math Grade 8 Lesson 2.2 Answer Key Problem Solving, McGraw Hill Math Grade 8 Lesson 2.1 Answer Key Multiplying and Dividing Whole Numbers. algebraic rule of the dilation: (x, y) -> (1/4x, 1/4y), Question 11. 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. _____________. 325. cfelg. _____________, Answer: _____________. (-1, 1) Question 3. _____________, Explanation: (-4, 2) (x, y) -> (1/4x, 1/4y) perimeter of the image = 12 + 12 + 12 + 12 = 48, Question 20. a. Scale factor = 2 lesson 10 2 algebraic representations of dilations So we get our dilation tool out. A'((3.-15), (3.-12)) -> A'(-15, -12) Type below: _____ Answer: Green square -> (x, y) -> (2x, 2y) Question 9. B'(6, 18) (x, y) -> (x, y+6) (2, -2) The figure is dilated by a scale factor of 5 and rotated 90 clockwise. Algebraic Representations of Dilations Success for English Learners A dilation changes the size of a figure without changing its shape. figure D Stretch = Image Grows Larger Graphical features of functions, including maximums, minimums, intervals of increase and decrease along with domain and range are introduced. What will the dimensions of the new room be, in feet, in the new house? Explanation: k = \(\frac{2}{3}\), Next, Let us represent the dilation algebraically, using (-4, 0), Question 4. _____________. ________ feet, Question 9. Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? Scale factor of 1.5 'LODWLRQV3UDFWLFH 6. Triangle UVW has coordinates U(15, 9), V(6, 4.5), and W(18, -3). Type below: Coordinates after dilation \(\frac{1}{4}\) = \(\frac{1}{4}\) (x, y) -> (1.5x, 1.5y) The blue square is the preimage. Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. Sketch the image of the figure after the dilation. When k is greater than 1, the dilation is an enlargement by the scale factor k. Question 5. B(9, 3) B'(9 \(\frac{1}{3}\), 3 \(\frac{1}{3}\)) B'(3, 1) .. (2) coordinates for A endstream endobj 131 0 obj <>stream Question 4. When k is between 0 and 1, the dilation is a reduction by the scale factor k. Perimeter = ________ units The backdrop scale factor is 1/20, not 1/12, Question 12. 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 a. Coordinates after dilation 0 = -1/3 . _____________, 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? (x, y) -> (x+3, y+5), Question 5. The triangle ABC shown on the grid is the pre-image. Answer: Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. Original perimeter: 16 dilation with a scale factor of 0.5 Type below: (-4, -2) The square is dilated under the dilation (x, y) (0.25x, 0.25y). Question 6. Translate the image 3 units down and 6 units right and dilate it by a factor of 2 Complete the table by writing same or changed to compare the image with the original figure in the given transformation. Type below: _____________, Explanation: Type below: _____________, Answer: Blueprint dimensions: 6.25 in. Time Squared Activity: Each participant gets 3 pages with 24 squares representing the hours in a day. a year ago. View this Page Yes; Quadrilateral DEFG is a dilation of quadrilateral DEFG. length |QR| = |8.75 2.5| = 6.25 inch horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. _____________. (x, y) -> (1.5x, 1.5y) (x, y) -> (x +5, y-6), Question 3. (x, y) (\(\frac{3}{2}\)x, \(\frac{3}{2}\)y) Image perimeter: _________, Answer: Options: D: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y) -4/-2 =2; 4/2 = 2 d = \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\) Translate the image 3 units down and 6 units right and dilate it by a factor of 2 _____________, Answer: (5, 5) Worksheets are Algebraic representati. ratio of y-coordinates = -4/-2 = 2, Question 2. The grid shows a diamond-shaped preimage. The scale factor of the dilation is _______. _____________, Explanation: (x, y) -> (2.5x, 2.5y) Describe how the graph of y = x shown at the right is changed through each of the following transformations. Image perimeter: 32, Explanation: (x, y) -> (-x, y); (x, y) -> (3x, 3y) Find the scale factor and the perimeter of each square. b. _____________, Answer: 18/4 = 4.5 mm (-4, 2) Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? A: (x, y) (-x, y) Example 10.2.1 Solve for in the equation . ratio of y-coordinates = 4/2 = 2 _____________. The dilation should be centered at 9, negative 9, and have a scale factor of 3. The triangles have only one pair of congruent angles, Question 2. _____________. 2x = 6 https://www.emathinstruction.com . Picture below shows the image of the figure before and after dilation. Mathematics. Find the angle measures of the actual sign. No; the dilation is not the same reversed, Explanation: What is the algebraic representation of this dilation? _____________, Answer: Question 7. 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) (7, 8) _____________, Answer: b. 2), (3.6)) -> B'(6, 18) scale factor = 1/2, Question 19. Area = ________ square units, Answer: a = 5, Question 5. Image perimeter: 48, Explanation: (-4, 0), Question 4. (0, 4) (0, -4) ratio of y-coordinates = 4/2 = 2 (-2, 0) Painted replica is 20 feet long and 16 feet high The actual building measures 400 feet long and 320 feet high. Original perimeter: _________ If the center of dilation is the origin and the scale factor is 3, graph the dilated image P'Q'R'. x + 1 Algebraic Representations of Dilations Practice and Problem Solving: D Use triangle ABC for Exercises 1-4. T'(2.5, 6.25), Question 9. The scale factor of the dilation is 2. Critical Thinking Explain how you can find the center of dilation of a triangle and its dilation. b. (0, 1) A (3, 3) 2 = 4. Graph the image of each figure after a dilation with the origin as its center and the given scale factor. (3, 4) (x, y) (2.5x, 2.5y) Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Type below: Type below: B: Rotate the square 180 around the origin. Options: Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. Question 12. Answer: Divide a side length of the dilated figure by the corresponding side length of the original figure. Type below: _____________, Question 12. _____________, Answer: F (3, 3) Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. Displaying all worksheets related to - Algebraic Representations Of Dialations. _____________, Answer: Name:&_____& &&&&&Date:&_____& Lesson:'10.2'Algebraic'Representations'of'Dilations'' Question 7. (-2, -2), Question 12. How can you use dilations to solve real-world problems? Describe the transformations that will transform the image back into the original figure. c. (x, y) -> (3x, 3y) Graph the image of XYZ after a dilation with a scale factor of \(\frac{1}{3}\) and the origin as its center. The actual building measures 400 feet long and 320 feet high. 1/3x = 1 Area = ________ square units, Answer: 1. d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Explanation: (x, y) -> (-x, y), Question 11. _____________. (x, y) -> (-y, x) _____________. Displaying all worksheets related to - Algebraic Representation Of Dialation. Options: How many feet? (1, 1) h24T0P044P06R Displaying all worksheets related to - Algebraic Representations Of Dilations. The figure is dilated by a scale factor of 5 and rotated 90 clockwise. 4. perimeter of the original square = 6 + 6 + 6 + 6 = 24 figure D a. y = 3x 1 Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. A square on the coordinate plane has vertices at (2, 2), (2, 2), (2, 2), and (2, 2). Answer: 5/2 = 2.5 (-1, 1) endstream endobj 136 0 obj <>stream In the given expression, we can notice that the x coordinate is multiplied with \(\frac{2}{3}\). (x, y) -> (1/4x, 1/4y) 10 x 10 = 7 x 2 = 10 x 9 = 5 x 8 = 10 x 3 = How did you do? b. 10.2 Algebraic Representation of Dilation - YouTube 8th grade go math 8th grade go math AboutPressCopyrightContact usCreatorsAdvertiseDevelopersTermsPrivacyPolicy & SafetyHow YouTube. Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity Online PDF to help the students to practice maths.