lesson 10 2 algebraic representations of dilations

BD/BD = 6/2 = 3 The business owner would like it on the top. (-2, 0) (1, -1) Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). Type below: Purple square -> (x, y) -> (1/2x, 1/2y), Question 6. Type below: class problems. The business owner wants it to remain on the left after the hypotenuse goes to the top. _____________, Answer: Perimeter = 8 units What is the algebraic representation of this dilation? What is the length of a side of the image? (x, y) -> (2.5x, 2.5y) Then write an algebraic rule to describe the dilation. _____________, Explanation: a. Type below: A dilation can produce a larger figure or an enlargement or a smaller figure or a reduction. The image is congruent to the original figure. lesson 10 2 algebraic representations of dilationsbsn sports track order numberbsn sports track order number Type below: (-2, 1) 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. (5, 5) _____________, Answer: A dilation with center (0, 0) and scale factor k is applied to a polygon. rotate 90counterclockwise, Question 4. Multiply each coordinate of the vertices of ABC by 2 to find the vertices of the dilated image A'B'C'. How does the dilation affect angle measures? b. (-2, -2), Question 12. Answer: Options: Answer: What is the scale factor in terms of inches to inches? b. y = \(\frac{1}{3}\)x + 1 coordinates for D 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 _______. (x, y) -> (x+3, y+5), Question 5. (x, y) (2x, 2y) _____________, Explanation: Question 7. 324, Algebraic Representations of Dilations Page No. ALGEBRAIC REPRESENTATIONS OF DILATIONS WORKSHEET Problem 1 : The triangle PQR shown on the grid is the pre-image. For example, if the scale factor is k, the algebraic representation of the dilation is Depending on the scale factor, dilation may increase or decrease the starting object. Type below: horizontally shrinks by a factor of 2/3, Question 12. A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. We have provided the Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity in the pdf format so that you can practice in online and offline mode. Answer: Answer: 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 . How can you use dilations to solve real-world problems? June 5, 2022 Posted by: Category: Uncategorized a. y = 2x + 6 (-1, -1) Scale factor: 2 y = -1/3 . 1. . translation 2 units left and 2 units up, Question 6. Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. 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 Type below: What are the vertices of the image? Critical Thinking A dilation with center (0,0) and scale factor k is applied to a polygon. S'(8.75, 6.25), Complete Lesson 9 4 Algebraic Representations Of Transformations Answer Key online with US Legal Forms. (-1, -1) 0 = 2/3 . Now, to return the dilated image to preimage having the coordinates of (kx, ky), dilate it by a scale factor \(\frac{1}{k}\), as shown below. and the ratio of the y-coordinates of corresponding points Type below: (show solution) FOCUS ON HIGHER ORDER THINKING Question 11 (request help) B'((3. (x, y) (-x, -y) C: (x, y) (x 5, y 6) T'(2.5, 6.25), Question 9. Type below: (0, 4) Type below: _____________, Answer: Find the lengths of the sides of the actual sign. x = 3 Test whether your answers are right or wrong with the help of the review test solutions. (-4, 2) original coordinates Scale factor = 2 Displaying all worksheets related to - Lesson Algebraic Representation Of Dilations 102. _____________, Question 9. Type below: (-2, -2) _____________, Answer: Question 2. Explanation A: The perimeter of the image is the perimeter of the original figure times the scale factor, Question 1. Graph the dilation. 2), (3.6)) -> B'(6, 18) Write the coordinates of the vertices of the preimage in the first column of the table. (3, 2), (1, 2), (3, 1), (1, 1) _____________, Answer: Substituting the value of k Explanation: b. Which equation does not represent a line with an x-intercept of 3? 10 x 10 = 7 x 2 = 10 x 9 = 5 x 8 = 10 x 3 = How did you do? endstream endobj 131 0 obj <>stream The dilation should be centered at 9, negative 9, and have a scale factor of 3. (9, 6), (3, 6), (9, 3), (3, 3) Original perimeter: 16 height: |QT| = |6.25 2.5| = 3.75 inch D: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y) algebraic rule: (x, y) -> (1/3x, 1/3y), Question 4. 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. Multiply each coordinate of the vertices of ABC by 3 to find the vertices of the dilated image. Question 4. For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates. c. y = \(\frac{2}{3}\)x 2 perimeter of the original square = 6 + 6 + 6 + 6 = 24 The grid shows a diamond-shaped preimage. h27P0P0P02V0T05U0R0QP0J'A@PE0I8tc ! C(3, 9) C'(3 \(\frac{1}{3}\), 9 \(\frac{1}{3}\)) C'(1, 3) (3) k = \(\frac{2}{3}\), Next, Let us represent the dilation algebraically, using C = (-2, -4), C = (-1, -2); 10.2 Algebraic Representations of Dilations. Green square: (x, y) (2x, 2y) The coordinates of the vertices of the original image are multiplied by _1 2 The dilation affect the length of line segments. The sides are proportional. 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. 2x = 6 d. (15, 10), (5, 10), (15, 5), (5, 5), Answer: (1, -1). Lesson 16 - Combining Dilations (Notes, Key) 10. Therefore, MNPQ is not a dilation of MNPQ, Question 8. -a + 7 = 2a 8 (2, 2) coordinates for C x = 1/3, Question 6. Answer: G(5, 2) G'(5 1.5, 2 1.5) G'(7.5, 3) (2) If two figures are similar but not congruent, what do you know about the sequence of transformations used to create one from the other? ratio of x-coordinates = -2/-1 = 2 Some dilations are reductions. The center of dilation is the origin. 7. c. What are the perimeter and area of the preimage? Section 10.3: Similar Figures. Reflection over x-axis (x, y) -> (x, -y) (-4, 3) _____________, Answer: endstream endobj 132 0 obj <>stream (0, -3) Firstly, we will write the coordinates of the vertices of the preimage. Thus, the dilation has no effects on the measures of the angles of the image. _____________, Answer: _____________. C. Apply the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. Question 5. B = (4, 2), B = (2, 1); (5, -3), Question 5. (x, y) (0.8x, 0.8y) Type below: Area = ________ square units, Answer: C (7.5, 6) x = 3 A(0, 2) A'(0, 4) A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). B'(6, 18) Mod 20-2 Class Problems. Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. a = 5, Question 5. a = 5, Question 5. Students use algebraic representations of dilations worksheet is a grid units. Answer: Type below: Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). (-2, 2) 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 + 1 b. y = \(\frac{1}{3}\)x + 1 b. Each coordinate of Triangle UVW is 3/4 times the corresponding coordinate of Triangle UVW. 90 clockwise rotation, Question 12. Options: Therefore, MNPQ is not a dilation of MNPQ, Question 8. 2/3x = 2 Explain how this can happen. 37, 53, and 90, Question 6. _____________. (x, y) -> (1.5x, 1.5y) (x, y) -> (1.5x, 1.5y) What are the vertices of the dilated image? The stage crewmembers calculation is incorrect. coordinates for B Type of function: Justification: 10. . 20.2 Algebraic Representations of Dilations. R'(8.75, 2.5), (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y), Question 6. The figure is dilated by a scale factor of 0.5 and translated 6 units left and 3 units up. Answer: Sketch the image of the figure after the dilation. 3/2 Therefore, we can conclude that the algebraic transformation rotated a figure counterclockwise for 90. figure B (Example 1). A'((3.-15), (3.-12)) -> A'(-15, -12) Identify a sequence of two transformations that will transform figure A into the given figure. h2V0Pw/+Q0L)0 coordinates for B _____________, Answer: Type below: Type below: Explain. No; the dilation is not the same reversed, Explanation: \(\frac{1}{4}\) = \(\frac{1}{4}\) Reflect the drawing over the x-axis Image perimeter: _________, Answer: The algebric dilation is (x, y) (48x, 48y). Label each image with the Answer: (-6, -1) For enlargements, k > 1. e. (x, y) (0.5x, 1.5y) C (7.5, 6) (9, 6), (3, 6), (9, 3), (3, 3), Question 2. (-4, 2) 320, Algebraic Representations of Dilations Page No. ratio of y-coordinates = 4/2 = 2 90 clockwise rotation, Question 12. _____________, Answer: 3x = 1 21.1 Parallel Lines Cut by a Transversal. Multiply each coordinate by the scale . Question 5. Type below: c. Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image. 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) c. a = 5 What will the dimensions of the new room be, in feet, in the new house? endstream endobj 133 0 obj <>stream After dilation figure D Scale factor of 1.5 MNOP has vertices at M(4.5, 6), N(9, 6), O'(9, 10.5), and P'(4.5, 10.5). Dilation is a process of changing the size of an object while the object remains in the same Shape. (x, y) (y, -x) Graph the image of each figure after a dilation with the origin as its center and the given scale factor. _____________. (x, y) -> (-x, y); (x, y) -> (x, 3y) Type below: Triangle XYZ has angles measuring 54 and 29. _____________. (x, y) -> (2.5x, 2.5y) 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: Both Triangle S have Angle S of measures 38, 67 and 75. A(1, 5) A'( 2 1, 2 5) A'(- 2,- 10) .. (1) B (7.5, 3) (3, 4) Perimeter = 2l + 2w = 2(8) + 2(8) = 32 [GET] Lesson 10.2 Practice B Geometry Answers Pages 603-611 A 4 B 5 C 5.62 D 6.31 E 5.83 8. (-2, 0) _____________, Question 12. 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. Type below: (-4, 4) Multiply each coordinate of the vertices of triangle ABC by \(\frac{1}{3}\) to find the vertices of the dilated image. (-6, 1), Question 13. Question 1. Type below: (x, y) -> (1.5x, 1.5y) A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). b. Answer: (-3, -4) If you draw a line connecting each pair of corresponding vertices, the lines will intersect at the center of dilation, Question 20. B: Rotate the square 180 around the origin. _____________, Explanation: _____________, Answer: Also, get the solutions to the review test on our Go Math Grade 8 Answer Key. Worksheets are Lodwlrqv3udfwlfh, Do not edit changes must be made through file info, Correctionkeyb transformations and similarity module 10, Graph the image of the figure using the transformation, Pre algebra, Lesson algebraic representations of transformations 9 4, Translations of shapes, Trainerinstructor notes . (-1, -1) _____________, Answer: The square is dilated under the dilation (x, y) (0.25x, 0.25y). Perimeter = 8 units During the video lesson have students: Take notes on the material. The blue square is the preimage. Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. Options: Type below: x = 3 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. e. What are the dimensions of the new room, in inches, on the blueprint? A'(-\(\frac{1}{2}\), 1) , B'(\(\frac{1}{2}\), 1) C'(0, -1). area = l.w = 8 .8 = 64, Question 6. Answer: Find the scale factor and the perimeter of each square. House dimensions: 25ft by 15ft, Question 10. Dilate each figure with the origin as the center of dilation. 1/3x = 1 After dilation -4/-2 =2; 4/2 = 2 What is the effect of a negative scale factor? Algebric rule of dilation will be (x, y) (\(\frac{1}{4}\)x, \(\frac{1}{4}\)y), Question 11. The blueprints are plotted on a coordinate plane. Type below: x = 3 Unit 9 Review. Describe the image of a dilation with a scale factor of 1. Two triangles, Triangle 1 and Triangle 2, are similar. AB/AB = 2/4 = 1/2 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. (x, y) -> (x +5, y-6), Question 3. Yes; Quadrilateral DEFG is a dilation of quadrilateral DEFG. d. (x, y) (\(\frac{2}{3}\)x, y) (-1, -1) Scale factor: ________, Question 9. The blue square is the preimage. _____________, Explanation: (0, -4) _____________, Explanation: This is called a reduction. Worksheets are Algebraic representati. What is the scale factor in terms of inches to inches? c. Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image. (0, -4) scale factor = 3, Explanation: Type below: 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. (x, y) -> (2x, 2y), Question 9. ! " (5, -3), Question 5. _____________, Answer: D. Sketch the image after the dilation on the coordinate grid. a dilation produces an image similar to the original figure, Question 10. perimeter of the image = 12 + 12 + 12 + 12 = 48, Question 20. Page 338: Performance Tasks. (2x, 2y) 5. So, the corresponding S are congruent. Which equation does not represent a line with an x-intercept of 3? Edit. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . by 3.75 in. _____________, Answer: _____________, Answer: What is the effect of a negative scale factor? Type below: (x, y) (kx, ky) Emathinstruction Algebra 1 Unit 10 Answer Key. (Explore Activities 1 and 2) Filled table is shown in the picture below. 15/5 = 3 mm Type below: Complete the table by writing same or changed to compare the image with the original figure in the given transformation. What is the effect of a negative scale factor? Page 335: Study Guide Review: Module 9. Write the algebraic representation of the dilation shown. _____________, Answer: Type below: But before this, let us soLve first the length of one side of the dilated image and the corresponding length of the originaL image using the distance formula C: (x, y) (x 5, y 6) a dilation produces an image similar to the original figure, Question 10. 324, Algebraic Representations of Dilations Page No. scale factor of \(\frac{1}{3}\) _____________. Type below: Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 13.2 Answer Key Algebraic Representations of Dilations. Multiply each coordinate of the vertices of rectangle FGHI by 1, 5 to find the vertices of the dilated image. Type below: Type below: The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals _______. y = 3x 1 Echocardiography technique, C'((3. 4), (3.-3)) -> C'(12, -9), Question 7. y = -1/3 . lesson 10 2 algebraic representations of dilations. B. A(-5, -4) A'(3 (-5), 3 (-4)) A'(-15, -12) (1) The business owner wants it to remain on the left after the hypotenuse goes to the top. 325, Algebraic Representations of Dilations Lesson Check Page No. e. What are the dimensions of the new room, in inches, on the blueprint? Type below: Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? _____________. y = 2/3 . The center of dilation is the origin and (x, y) (3x, 3y). LESSON 10-2 . algebraic rule: (x, y) -> (1/3x, 1/3y), Question 4. The dimension of a new room on a blueprint is now: ________ inches Examples, solutions, videos, worksheets, games, and activities to help geometry students learn. 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. (-7, -4) (3, 8) (-2.5, 2.5) MN = \(\sqrt{(3)^{2}+(0)^{2}}\) (1, 1) _____________, Answer: b. a translation down 3 units Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. d. (x, y) (\(\frac{2}{3}\)x, y) Question 9. Lets find the ratio of length \(\frac{20}{400}\) = \(\frac{1}{20}\) After the sequencing of transformations, reflection over the y-axis. (1, -1). Type below: by 3.75 in. 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) Edit. B: Rotate the square 180 around the origin. Type below: _____________. coordinates for C MN/MN = 3/4.5 = 2/3 Download Go Math Grade 8 Chapter 10 Transformations and Similarity Answer Key PDF and begin your practice. Type below: _____________, Answer: A'(-15, -12) (x, y) -> (x, -y); (x, y) -> (3x, 3y), Question 4. Triangle XYZ has angles measuring 54 and 29. The vertices of the dilated image are F'(3.5, 3.5), G'(7.5, 3.5), H'(7.5, 6) and I'(, 9). 326, Similar Figures Lesson Check Page No. The ratios of the lengths of the corresponding sides are not equal. b. The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals _______. Apply the indicated sequence of transformations to the square. 2 = 4. A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. Page 337: Study Guide Review: Module 10. houses for sale chepstow moon and co. shani hardwick wilson obituary Be the first person to grab Go Math Grade 8 Answer Key Chapter 10 Transformations and Similarity to score good marks in the exam. Date Class LESSON Algebraic Representations of Dilations Reteach You dilate a figure using the origin as the center of . Explain. A dilation of the square has vertices at (6, 6), (6, 6), (6, 6), and (6, 6). When a dilation in the coordinate plane has the origin as the center of dilation, we can find points on the dilated image by multiplying the x and y coordinates of the original figure by the scale factor. The angle measures are the same Represent Real-World Problems The blueprints for a new house are scaled so that \(\frac{1}{4}\) inch equals 1 foot. Question 6. A rectangle has vertices (6, 4), (2, 4), (6, 2), and (2, 2). ________ feet, Question 9. ratio of x-coordinates = ____________ c. (x, y) (x, 2y) Type below: LJKG i 80`- wMK0,7 {1L`j7 Fi@W_w ~H; po0]uWuvGG]nB\9LgxG:1~}_ G The figure is reflected across the y-axis and dilated by a scale factor of 4. Length of MN, given M(4.5, 6), N(9, 6). No; one figure is not a dilation of the other, Explanation: MN = 3, Now, let us determine the value of k, that is endstream endobj 136 0 obj <>stream d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Answer: (x, y) -> (x+6, y-3) Find the scale factor and the perimeter of each square. Triangle UVW has coordinates U(15, 9), V(6, 4.5), and W(18, -3). dilation with a scale factor of 0.5 The figure and its final image are congruent. Image perimeter: 48, Explanation: Graph the image of XYZ after a dilation with a scale factor of \(\frac{1}{3}\) and the origin as its center. The square is dilated under the dilation (x, y) (0.25x, 0.25y). 130 0 obj <>stream Determine whether the given representation is representative of a linear, exponential, or quadratic function. In this lesson, you will learn multiples of 11. vertically stretches by a factor of 2, Question 12. _____________. _____________, Answer: > ~ y o