The blueprint is the preimage and the house is the dilated image. 2x = 6 Dilation is defined as a transformation that changes the size of a figure. For each pair of corresponding vertices, find the ratio of the x-coordinates and the ratio of the y-coordinates. Answer: (0, 1) ALGEBRAIC REPRESENTATIONS OF DILATIONS 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. Original perimeter: _________ D. Sketch the image after the dilation on the coordinate grid. Find the angle measures of the actual sign. (x, y) (y, -x) Lesson 2: Algebraic Representations of Dilations, Question 1. 10cm 40 = 400cm (0, -4) f& b. B: Rotate the square 180 around the origin. Transformations (including Dilations): 16.1 And 16.2 - Quizlet. 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. Which equation does not represent a line with an x-intercept of 3? The blueprints are plotted on a coordinate plane. A square on the coordinate plane has vertices at (3, 3), (3, 3), (3, 3), and (3, 3). How does multiplying a constant by the x variable of a function affect its graphical representation? Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. (-4, 2) (7, 4) -6/-3 =2; 6/3 = 2 130 0 obj <>stream The first idea is that we can construct representations of relationships between two sets of quantities and that these representations, which we call functions, have common traits. To create the actual sign shown, the drawing must be dilated using a scale factor of 40. D: (x, y) (\(\frac{1}{2}\)x, \(\frac{1}{2}\)y) endstream endobj 134 0 obj <>stream (x, y) -> (-x, y); (x, y) -> (x, 3y) Type below: Answer: (2x, 2y) 5. Dilate each figure with the origin as the center of dilation. b. The ratio of the lengths of the corresponding sides of triangle ABC and triangle ABC equals 2. (-2, 0) (x, y) (2x, 2y) Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure. _____________. Type below: Type below: The square is dilated under the dilation (x, y) (0.25x, 0.25y). When taking . 8th grade. Describe the image of a dilation with a scale factor of 1. So, the scale factor of the dilation is 3/4. a. a = -3 More lesson videos. When k is between 0 and 1, the dilation is a reduction by the scale factor k. Find the lengths of the sides of the actual sign. 21.1 Parallel Lines Cut by a Transversal. each side of the second figure is 1.25 times the corresponding side of the original figure. Type below: (2, 2) (x, y) -> (1/3x, 1/3y), Question 8. B: Rotate the square 180 around the origin. _____________, Explanation: Options: H (7.5, 6) b. G (7.5, 3) Type below: d. What are the perimeter and area of the image? Triangle UVW has coordinates U(15, 9), V(6, 4.5), and W(18, -3). (9, 6), (3, 6), (9, 3), (3, 3) (2, -1) Stretch = Image Grows Larger Explanation A: Lesson Title: Transformations of Functions Part 2: Dilations Date:_____ Subject: Algebra I or Algebra II T. opic: Translations of Functions. If the scale factor k is between 0 and 1 the image is a reduction. _____________, Answer: _____________, Explanation: Solve a + 7 = 2a 8. Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. The ratios of the lengths of the corresponding sides are not equal. 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. 8cm 40 = 320cm (-1, 1) ______ units, Question 6. Perimeter = 32 units _____________. e. What are the dimensions of the new room, in inches, on the blueprint? 6cm 40 = 240cm The backdrop scale factor is 1/20, not 1/12, Question 12. _____________, Answer: . Write the algebraic representation of the dilation shown. In Exercises 710, the transformation of a figure into its image is described. d. A rectangular room has coordinates Q(2, 2), R(7, 2), S(7, 5), and T(2, 5) on the blueprint. ratio of x-coordinates = _______ Example 10.2.1 Solve for in the equation . What is the algebraic representation of this dilation? coordinates for C Classify each as such and justify your reasoning. How would a dilation with scale factor 1 affect the preimage? G(5, 2) G'(5 1.5, 2 1.5) G'(7.5, 3) (2) Answer: ratio of y-coordinates = -4/-2 = 2, Question 2. 21.1 Parallel Lines Cut by a Transversal. Download Go Math Grade 8 Chapter 10 Transformations and Similarity Answer Key PDF and begin your practice. Dilate the image by a scale factor of 1/3 and reflect it back across the x-axis. (x, y) -> (2x, 2y), Question 9. c. Write the algebraic representation of the dilation from the blueprint to the house. Answer: (0, 4) Mod20-2Notes. Area = ________ square units, Answer: (x, y) (x, 2y) Multiply each coordinate of the vertices of rectangle FGHI by 1, 5 to find the vertices of the dilated image. (-2, 0) 326, Similar Figures Lesson Check Page No. Options: lesson 10 2 algebraic representations of dilationsppl center view from my seatppl center view from my seat coordinates for B scale factor of 1.5 a year ago. List the coordinates of the vertices of the preimage in the first column of the table. (2, -1) Type below: a. Perimeter = 8 units (-7, -8) _____________, Explanation: The dilation should be centered at 9, negative 9, and have a scale factor of 3. Save. d. (x, y) (\(\frac{2}{3}\)x, y) If you draw a line connecting each pair of corresponding vertices, the lines will intersect at the center of dilation, Question 20. A rectangle has vertices (6, 4), (2, 4), (6, 2), and (2, 2). a. a dilation by a scale factor of 4 7. The best learning comes with the best learning guide. C (7.5, 6) Options: Triangle XYZ has angles measuring 29 and 92. Explanation: perimeter of the original square = 4 + 4 + 4 + 4 = 16 (-2, 2) Test whether your answers are right or wrong with the help of the review test solutions. How does the dilation affect the length of line segments? Type below: (-4, -2), Question 12. Determine whether one figure is a dilation of the other. Answer: Type below: For example, if the scale factor is k, the algebraic representation of the dilation is d. A rectangular room has coordinates Q(2, 2), R(7, 2), S(7, 5), and T(2, 5) on the blueprint. Answer: The center of dilation is the origin. Displaying all worksheets related to - Lesson Algebraic Representation Of Dilations 102. What are the coordinates of the new room? House dimensions: 25ft by 15ft, Question 10. 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. _____________, Answer: _____________, Answer: Multiply each coordinate by the scale . x = 3 Scale factor: _________ Algebraic Representations of Dilations - 2. Explain your reasoning. Question 6. To calculate the verticies of the image after dilation, we will use following rule: Type below: Make a Conjecture coordinates for D b. Image perimeter: _________, Answer: c. (x, y) (x, 2y) The business owner would like it on the top. (x, y) -> (x +5, y-6), Question 3. Type below: Multiple Choice Use the diagram below to find the value of x. . Original perimeter: _________ d. (x, y) -> (x, -y); (x, y) -> (3x, 3y), Answer: Describe two transformations that will do this. 0 = -2x + 6 If the scale factor is greater than 1, the image is an enlargement. The figure and its final image are congruent. The center of dilation is the origin and (x, y) (3x, 3y). a dilation produces an image similar to the original figure, Question 10. 332, 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. At least one transformation must be a dilation with a scale factor other than 1, Question 6. Explain. b. _____________, Answer: Type below: This will be followed by the. (-4, 0), Question 4. Green square -> (x, y) -> (2x, 2y) C(4, -3) C'(3 4, 3 (-3)) C'(12, -9) .. (3) Critical Thinking MNOP has vertices at M'(3, 4), N'(6, 4), O'(6, 7), and P'(3, 7). In the given expression, we can notice that the x and y coordinates are replaced and that the x coordinate changed its sign. c. Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image. Type below: _____ Answer: Green square -> (x, y) -> (2x, 2y) _____________, Answer: (5, 5) Page 335: Study Guide Review: Module 9. Type below: Therefore, we can conclude that dilation affects the length of line segments by either increasing or decreasing their length. Image perimeter: _________, Answer: scale factor = 3, Explanation: Perimeter = ________ units (-6, 1), Question 13. (4, 0) Lesson 13.2 Algebraic Representations of Dilations Lesson 13.3 Dilations and Measurement Texas Go Math Grade 8 Module 13 Quiz Answer Key Texas Go Math Grade 8 Unit 5 Study Guide Review Answer Key Texas Go Math Grade 8 Teacher Edition Answer Key Unit 6 Statistics and Samples Module 14 Scatter Plots _____________, Explanation: Type below: The grid shows a diamond-shaped preimage. Is the crewmembers calculation correct if the painted replica is to cover the entire backdrop? A dilation of (x, y) (kx, ky) when 0 < k < 1 has what effect on the figure? (-2, 0) The Go Math Grade 8 Solution Key Chapter 10 Transformations and Similarity help the students to enhance their math skills. x = 2 . (x, y) (0.5x, 1.5y) Write the coordinates of the vertices of the preimage in the first column of the table. (x, y) (\(\frac{2}{3}\)x, \(\frac{2}{3}\)y). Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square.
