lesson 10 2 algebraic representations of dilations
A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. (x, y) -> (2.5x, 2.5y) (x, y) (y, -x) B: Rotate the square 180 around the origin. Since it changes the size of a figure, it has no something to do with the changes when it comes to the angles of the image. 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. _____________, Answer: (x, y) -> (1/3x, 1/3y), Question 8. After dilation: (x, y) -> (x+3, y+5), Question 5. Apply each transformation to the image of the previous transformation. _____________, Answer: MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). Dilation Geometry Definition: A dilation is a proportional stretch or shrink of an image on the coordinate plane based on a scale factor. (x, y) -> (2.5x, 2.5y), Question 3. 325. . Perimeter = 2l + 2w = 2(2) + 2(2) = 8 b. y = \(\frac{1}{3}\)x + 1 H (7.5, 6) c. What are the perimeter and area of the preimage? (-1, -1) 715 Module 20 Lesson 2 Algebraic Representation of Dilation DRAFT. c. (x, y) (x, 2y) (x, y) -> (1.5x, 1.5y) Orientation of the figure in the coordinate plane is rotated 180. c. a reflection across the y-axis a = 5, Question 5. Perimeter = ________ units Thus, the dilation has no effects on the measures of the angles of the image. (2, -2) What is the length of a side of the image? e. (x, y) (0.5x, 1.5y) Mike DeVor. d. a = 15, Explanation: Type below: Answer: C'(12, -9), Explanation: Algebraic Representations of Dilations Practice and Problem Solving: A/B Use triangle ABC for Exercises 1-4. Worksheets are Middle school math series course 2, Chapter 7, Algebraic representations of dilations, Algebraic representations of dilations, Conjectures. (9, 6), (3, 6), (9, 3), (3, 3), Question 2. b. a translation down 3 units y = -2x + 6 (x, y) -> (-y, x) C: (x, y) (x 5, y 6) BD/BD = 6/2 = 3 I know that triangle ABC is a dilation of triangle ABC because the ratios of the corresponding x-coordinates are equal and the ratios of the corresponding y-coordinates are equal. endstream endobj 136 0 obj <>stream The perimeter of the image is the perimeter of the original figure times the scale factor, Question 1. meaning that we will multiply every coordinate with \(\frac{3}{2}\). Clifford Algebras - Daniel Klawitter 2014-10-29 After revising known representations of the group of Euclidean displacements Identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3. MN/MN = 3/4.5 = 2/3 What will the dimensions of the new room be, in feet, in the new house? _____________, Answer: a. a = -3 The angle measures are the same Problem 1 What are the characteristics of an enlargement? Type below: Justify your answer. How many feet? Find the angle measures of the actual sign. (3, 4) (-2, 1) (-4, -2), Question 12. Question 3. d. y = 3x 1, Explanation: (0, 4) ratio of x-coordinates = -4/-2 = 2 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. lesson 10 2 algebraic representations of dilations. Multiply each coordinate of the vertices of rectangle QRST by 125% = \(\frac{125}{100}\) = \(\frac{5}{4}\) to find the vertices of the dilated image. The homeowner wants this room to be 25% larger. b. a = \(\frac{1}{3}\) d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Explanation: Algebra Review. Given M(4.5, 6), N(9, 6), 0(9, 10.5), P(4.5, 10.5) and M'(3, 4), N'(6, 4), O'(6, 7), M(3, 7) center at the origin, Let us represent the dilation algebraically. B = (4, 2), B = (2, 1); What is the effect on the figure when k > 1? B: Rotate the square 180 around the origin. Question 9. The lengths are 240 cm, 320 cm, and 400 cm, Question 6. Describe two transformations that will do this. The dimension of a new room on a blueprint is now: (x, y) -> (x, -y) Lesson 2: Algebraic Representations of Dilations, Question 1. y = 2/3 . G (7.5, 3) (-4, -2) I know that triangle ABC is a dilation of triangle ABC because the ratios of the corresponding x-coordinates are equal and the ratios of the corresponding y-coordinates are equal. Test whether your answers are right or wrong with the help of the review test solutions. Type below: The center of dilation is the origin and (x, y) (3x, 3y). b. Question 7. MN = \(\sqrt{(9-4.5)^{2}+(6-6)^{2}}\) If the scale factor k is between 0 and 1 the image is a reduction. When k is between 0 and 1, the dilation is a reduction by the scale factor k. Question 2. Then write an algebraic rule to describe the dilation. The figure is reflected across the y-axis and dilated by a scale factor of 4. Picture below shows the image of the figure before and after dilation. 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 is the same shape but a different size than quadrilateral MNPQ. Triangle XYZ has angles measuring 54 and 29. Displaying all worksheets related to - Lesson Algebraic Representation Of Dilations 102. Substituting the value of k B(9, 3) B'(9 \(\frac{1}{3}\), 3 \(\frac{1}{3}\)) B'(3, 1) .. (2) Multiply each coordinate of the vertices of ABC by 2 to find the vertices of the dilated image A'B'C'. Type below: (1, -1). Type below: (x, y) (y, -x) Answer: Label each image with the (-1, 1) _____________, Explanation: Question 3. Length of MN, given M(4.5, 6), N(9, 6). b. 20.2 Algebraic Representations of Dilations. (2, 2) Answer: Complete Lesson 9 4 Algebraic Representations Of Transformations Answer Key online with US Legal Forms. lesson 10 2 algebraic representations of dilationsmercedes financial services phone numbermercedes financial services phone number b. x 2 (x, y) (kx, ky) 8cm 40 = 320cm 3a = 15 _____________, Answer: _____________, Answer: Image perimeter: 32, Explanation: The business owner would like it on the top. What is the scale factor in terms of inches to inches? 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 . Reflect the drawing over the x-axis 5/2 = 2.5 a. Perimeter = ________ units h24T0P044P06R The triangles have only one pair of congruent angles, Question 2. Type below: coordinates for A ABC(x,y) * (x,y. Answer: ratio of x-coordinates = -2/-1 = 2 S'(8.75, 6.25), The figure is reflected across the y-axis and dilated by a scale factor of 4. endstream endobj 135 0 obj <>stream Complete the table by writing same or changed to compare the image with the original figure in the given transformation. Type below: algebraic rule of the dilation: (x, y) -> (1/4x, 1/4y), Question 11. k = \(\frac{3}{4.5}\) Make a Conjecture c. Write the algebraic representation of the dilation from the blueprint to the house. (x, y) -> (-x, y); (x, y) -> (x, 3y) The blue square is the preimage. The center of dilation is the origin and (x, y) (3x, 3y). Answer: (-2.5, 2.5) Sketch the image of the figure after the dilation. ______ units, Question 6. 13.2. (x, y) -> (2x, 2y), Question 9. (5, 5) _____________, Answer: (x, y) -> (x+6, y-3) When taking . Type below: 7. Explanation: By, definition of a dilation in which it can only be enlarged or reduced with respect to the scale factor k between 0 and 1 or greater than 1, respectively, if the scale factor in the dilation is equal to 1, then the image would be the same as the preimage. After the sequencing of transformations, reflection over the y-axis. facial recognition time clock no monthly fee; mower deck spindle replacement D. Sketch the image after the dilation on the coordinate grid. 3x = 1 (9, 6), (3, 6), (9, 3), (3, 3) Two triangles, Triangle 1 and Triangle 2, are similar. _____________, Question 12. 8.10.C: Description: explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90, 180, 270, and 360 as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; and . 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. Scale factor = 2 Therefore, we can conclude that the algebraic transformation rotated a figure counterclockwise for 90. 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 . letter of the transformation applied. _____________, Answer: Save or instantly send your ready documents. Find the scale factor and the perimeter of each square. Explain how this can happen. Type below: each side of the second figure is 1.25 times the corresponding side of the original figure. _____________, Answer: 324, Algebraic Representations of Dilations Page No. Scale factor = 2 _____________. A dilation of the square has vertices at (6, 6), (6, 6), (6, 6), and (6, 6). coordinates for B How can you describe the effect of a dilation on coordinates using an algebraic representation?. (x, y) (\(\frac{2}{3}\)x, y) Type below: _____ Answer: Green square -> (x, y) -> (2x, 2y) Type below: _____________, Explanation: Type below: scale factor = 3, Explanation: _____________, Answer: 10.2 Algebraic Representation of Dilation - YouTube 8th grade go math 8th grade go math AboutPressCopyrightContact usCreatorsAdvertiseDevelopersTermsPrivacyPolicy & SafetyHow YouTube. The figure is dilated by a factor of 2, but the orientation of the figure in the coordinate plane is rotated 180, Question 1. length |QR| = |8.75 2.5| = 6.25 inch (-4, 2) 23 times. lesson 10 2 algebraic representations of dilations class problems. C(4, -3) C'(3 4, 3 (-3)) C'(12, -9) .. (3) b. _____________. The blueprint is the preimage and the house is the dilated image. 1. lesson 10 2 algebraic representations of dilations The center of dilation is the origin. (5, -3), Question 5. _____________, Answer: Identify a sequence of two transformations that will transform figure A into the given figure. Students use algebraic representations of dilations worksheet is a grid units. _____________, Answer: d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Answer: _____________, Answer: 320, Algebraic Representations of Dilations Page No. Answer: ________ feet, Question 9. _____________. b. Solve a + 7 = 2a 8. a. B: Rotate the square 180 around the origin. Type below: _____________, Answer: horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. Type below: (0, -6) _____________, Answer: When k is between 0 and 1, the dilation is a reduction by the scale factor k. The figures are similar is they are the same shape but different size SO one is a dilation of the other, Question 11. ________. Options: A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). Perimeter = 8 units x = 1/3, Question 6. Type below: One inch on the blueprint represents how many inches in the actual house? (-6, -1) Image perimeter: _________, Answer: How many feet? cfelg. (7, 4) 10.2 Algebraic Representations of Dilations. The division process is straightforward. c. Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image. Our services run deep and are backed by over ten years of experience. ratio of y-coordinates = -4/-2 = 2, Question 2. e. (x, y) (0.5x, 1.5y) What are the coordinates? (x, y) (x, 2y) (-4, 2) a = 15/3 Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. (x, y) -> (-x, y), Question 11. Example 10.2.1 Solve for in the equation . 2), (3.6)) -> B'(6, 18) _____________, Answer: Download Go Math Grade 8 Chapter 10 Transformations and Similarity Answer Key PDF and begin your practice. 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. Scale factor: _________ ratio of x-coordinates = 2 Determine whether one figure is a dilation of the other. The drawing has sides measuring 6 cm, 8 cm, and 10 cm, and angles measuring 37, 53, and 90. a. a dilation by a scale factor of 4 examples of gram negative spore forming bacteria. On a coordinate plane, triangle UVW has coordinates U(20, 12), V(8, 6), and W(24, -4). A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). 2), (3.6)) -> B'(6, 18) The blueprints are plotted on a coordinate plane. 325, Algebraic Representations of Dilations Lesson Check Page No. Type below: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y), Question 6. scale factor = 1/2, Question 19. _____________, Answer: _____________, Answer: Type below: The backdrop scale factor is 1/20, not 1/12, Question 12. If the dilation produce a larger figure the line segments of the dilated figure is longer than the original figure Also, if the dilation produce a smaller figure, the line segments of the dilated figure is smaller than the original figure. You are here: Home 1 / Clearway in the Community 2 / Uncategorised 3 / lesson 10 2 algebraic representations of dilations. Rotate the drawing 180 around the origin. (x, y) -> (x+3, y+5), Question 5. Lets find the ratio oft: x-coordinates of corresponding points (x, y) -> (x, y+6) Graph the image of the figure using the transformation given. (-4, 0), Question 4. The center of dilation is the origin and (x, y) (3x, 3y). 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. In the given expression, we can notice that the x coordinate is multiplied with \(\frac{2}{3}\). What are the vertices of the dilated image? Answer: B'((3. Options: Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. 0 = -1/3 . 24/8 = 3 mm c. (x, y) -> (3x, 3y) x 2 Question 16. a. (0, 4) Scale factor: 2 Perimeter = 2l + 2w = 2(8) + 2(8) = 32 Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). _____________. _____________, Explanation: Scale factor = 2 LJKG i 80`- wMK0,7 {1L`j7 Fi@W_w ~H; po0]uWuvGG]nB\9LgxG:1~}_ G
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