lesson 10 2 algebraic representations of dilations

Question 2. Question 12. d. (15, 10), (5, 10), (15, 5), (5, 5), Answer: ratio of x-coordinates = -4/-2 = 2 The perimeter of the image is the perimeter of the original figure times the scale factor, Question 1. Multiply each coordinate of the vertices of triangle ABC by $\frac{1}{3}$ to find the vertices of the dilated image. _____________, Answer: figure D List the coordinates of the vertices of the preimage in the first column of the table. (3, 8) The coordinates of the vertices of the original image are multiplied by 2 for the green square. 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. Type below: (5, 5) (x, y) -> (x, y+6) (x, y) (0.5x, 1.5y) Represent Real-World Problems The blueprints for a new house are scaled so that $\frac{1}{4}$ inch equals 1 foot. A: (x, y) (-x, y) a. a dilation by a scale factor of 4 Perimeter = ________ units The students can easily learn maths with the Go Math Grade 8 Solution Key. _____________. Make a Conjecture e. What are the dimensions of the new room, in inches, on the blueprint? (-1, -1) Triangle XYZ has angles measuring 54 and 29. _____________, Answer: The lengths are 240 cm, 320 cm, and 400 cm, Question 6. 1/3x = 1 Answer: What is the effect of a negative scale factor? Answer: So we get our dilation tool out. C. Apply the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. d. A rectangular room has coordinates Q(2, 2), R(7, 2), S(7, 5), and T(2, 5) on the blueprint. At least one transformation must be a dilation with a scale factor other than 1, Question 6. The Go Math Grade 8 Solution Key Chapter 10 Transformations and Similarity help the students to enhance their math skills. What dilation can you apply to the image to return it to the original preimage? 10/4 = 2.5 A dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction). If you draw a line connecting each pair of corresponding vertices, the lines will intersect at the center of dilation, Question 20. 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) _____________, Answer: Triangle XYZ has angles measuring 29 and 92. Scale factor of 1.5 Type below: 90 clockwise rotation, Question 12. After calculating the coordinates, we can graph every point of the image after dilation and connect them to get the wanted figure. The business owner wants it to remain on the left after the hypotenuse goes to the top. coordinates for D MNOP has vertices at M(4.5, 6), N(9, 6), O(9, 10.5), and P(4.5, 10.5). _____________, Explanation: Algebraic Representations of Dilations. Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? Dilate each figure with the origin as the center of dilation. Answer: 0 = 2/3 . 130 0 obj <>stream d. The shorter leg of the drawing is currently on the left. When a dilation in 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. (-7, -4) Type below: Answer: Type below: _____ Answer: Green square -> (x, y) -> (2x, 2y) (-6, -2) figure B Edit. y = -2x + 6 Dilation Geometry Definition: A dilation is a proportional stretch or shrink of an image on the coordinate plane based on a scale factor. After dilation: 326, Similar Figures Lesson Check Page No. _____________. a. Graph the image. Echocardiography technique, 8cm 40 = 320cm $\frac{1}{4}$ = $\frac{1}{4}$ Question 5. On a coordinate plane, triangle UVW has coordinates U(20, 12), V(8, 6), and W(24, -4). Quadrilateral MNPQ has side lengths of 5 mm, 8 mm, 7 mm, and 4 mm. figure C Answer: 3a = 15 _____________, Answer: algebraic rule: (x, y) -> (1.5x, 1.5y), Question 3. This is called a reduction. Picture below shows the image of the figure before and after dilation. A(0, 2) A'(0, 4) by 3.75 in. The homeowner wants this room to be 25% larger. Answer: Type below: S'(8.75, 6.25), T'(2.5, 6.25), Question 9. Answer: c. The drawing has the hypotenuse on the bottom. (2, -1) 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? So, to learn maths in the best way, you must refer to HMH Go Math Grade 8 Solution Key. d. What are the perimeter and area of the image? Solve a + 7 = 2a 8. For scale factor k, the algebraic representation of the dilation is (x, y) (kx, ky). Many students have loved the way of explanation given on Go Math Grade 8 Answer Key on our website. by 3.75 in. x + 1 21.1 Parallel Lines Cut by a Transversal. A dilation of the square has vertices at (4, 4), (4, 4), (4, 4), and (4, 4). a. Triangle UVW has coordinates U(15, 9), V(6, 4.5), and W(18, -3). Then write an algebraic rule to describe the dilation. Determine whether the given representation is representative of a linear, exponential, or quadratic function. No; one figure is not a dilation of the other, Explanation: 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 . b. (-3, -4) (4, 0) Let us determine the dilation than can be applied to the image to return it to the original preimage. (9, 6), (3, 6), (9, 3), (3, 3) No; the dilation is not the same reversed, Explanation: scale factor of $\frac{1}{3}$ Your service title Give us a brief description of the service that you are promoting. A stage crew member writes (x, y) ($\frac{1}{12}$x, $\frac{1}{12}$y) to represent the dilation. _____________, Answer: algebraic rule: (x, y) -> (2/3x, 2/3y), Question 8. _____________. A = (-4, 4), A = (-2, 2); (7, 4) coordinates for B What are the coordinates? 325, Algebraic Representations of Dilations Lesson Check Page No. Graph the image of each figure after a dilation with the origin as its center and the given scale factor. Dilation is a process of changing the size of an object while the object remains in the same Shape. (x, y) -> (x, y+6) Answer: Divide a side length of the dilated figure by the corresponding side length of the original figure. Options: Scale factor: _________ Page 337: Study Guide Review: Module 10. Explain how this can happen. Page 334: Mixed Review. Answer: a year ago. OL@6BxtiJZ7f)^H(pjl4.I`'Fq rm;`$PE\!0P{a!-;}])o1Y-f /PMM$4x*gv|DeF. |_]prV8!Q~~p Type below: _____________, Answer: Type below: (x, y) -> (-x, y), Question 11. 20.3 Similar Figures. 8th Grade Texas Mathematics: Unpacked Content 5. Look at the coordinates of corresponding vertices. The scale factor of the dilation is 2. 7. 2 7 3 12 4 19 5 28 Type of function: Justification: 8. A (0, 4), B (0, 0), C (5, 0) 2. Save or instantly send your ready documents. For scale factor k, the algebraic representation of the dilation is (x, y) (kx, ky). A: (x, y) (-x, y) horizontally shrinks by a factor of 0.5 and vertically stretches by a factor of 1.5, Question 13. (x, y) (2.5x, 2.5y) a. a dilation by a scale factor of 4 d. A rectangular room has coordinates Q(2, 2), R(7, 2), S(7, 5), and T(2, 5) on the blueprint. Explanation: (x, y) ($\frac{2}{3}$x, y) x = 2 . _____________, Answer: (x, y) -> (-y, x) y = -1/3 . The vertices of the dilated image are F'(3.5, 3.5), G'(7.5, 3.5), H'(7.5, 6) and I'(, 9). The figures are similar is they are the same shape but different size SO one is a dilation of the other, Question 11. Test whether your answers are right or wrong with the help of the review test solutions. _____________, Answer: a = 5, Question 5. 21.1 Parallel Lines Cut by a Transversal. (-1, -1) (-4, -2), Question 12. ratio of y-coordinates = _______ area = l.w = 8 .8 = 64, Question 6. Perimeter = 2l + 2w = 2(8) + 2(8) = 32 (1, -1). b. Type below: a. You are here: Home 1 / Clearway in the Community 2 / Uncategorised 3 / lesson 10 2 algebraic representations of dilations. House dimensions: 25ft by 15ft, Question 10. and find the ratio of heigh: $\frac{16}{320}$ = $\frac{1}{20}$ What is the scale factor in terms of inches to inches? (x, y) (y, -x) 10.2 Solving Exponential Equations - Intermediate Algebra. Coordinates after dilation Scale factor: ________, Question 9. ratio of x-coordinates = 4/2 = 2 C: (x, y) (x 5, y 6) For example, if the scale factor is "k", the algebraic representation of the dilation is For enlargements, k > 1 and for reductions, k Type below: Identify the scale factor used in each dilation. (-2, 2) LESSON 10-2 Practice and Problem Solving: A/B 1. R'(8.75, 2.5), Lesson Title: Transformations of Functions Part 2: Dilations Date:_____ Subject: Algebra I or Algebra II T. opic: Translations of Functions. Perimeter = ________ units lesson 10 2 algebraic representations of dilationsppl center view from my seatppl center view from my seat B: Rotate the square 180 around the origin. Type below: Answer: c. Write the algebraic representation of the dilation from the blueprint to the house. A. Answer: If the center of dilation is the origin and the scale factor is 3, graph the dilated image P'Q'R'. Type below: What is the algebraic representation of this dilation? Describe how the graph of y = x shown at the right is changed through each of the following transformations. This will be followed by the. vertically stretches by a factor of 2, Question 12. a. The ratios of the lengths of the corresponding sides are not equal. Reflect the drawing over the x-axis The corresponding angles of triangle ABC and triangle ABC are _______. Each case is succinctly presented in an easy-to-read question-answer, self-test format comprised of three printed pages of text and echo images. Perimeter = 8 units Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. Is this the same as translating the graph up 5 units and then dilating by a scale factor of 3? Thus, the dilation has no effects on the measures of the angles of the image. Sketch the image of the figure after the dilation. Critical Thinking A triangle has vertices A(-5, -4), B(2, 6), and C(4, -3). Which equation does not represent a line with an x-intercept of 3? Image perimeter: _________, Answer: Students use algebraic representations of dilations worksheet is a grid units. Answer: ratio of x-coordinates = -2/-1 = 2 Lets find the ratio of length $\frac{20}{400}$ = $\frac{1}{20}$ Quadrilateral MNPQ is the same shape but a different size than quadrilateral MNPQ. Question 6. _____________, Answer: Type below: A(8, 0) A' . a year ago. For example, if the scale factor is k, the algebraic representation of the dilation is *Click on Open button to open and print to worksheet. dilation with a scale factor of 0.5 320, Algebraic Representations of Dilations Page No. (0, -4) 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 _______. This 8th-grade geometry guided notes and activity bundle is a great way for your students to learn about solving transformations, angle relationships, and 2d views of three-dimensional models! _____________, Answer: Name:&_____& &&&&&Date:&_____& Lesson:'10.2'Algebraic'Representations'of'Dilations'' d. (x, y) -> (6x, 6y), Explanation: The figure is reflected across the y-axis and dilated by a scale factor of 4. The center of dilation is the origin and (x, y) (3x, 3y). Answer: 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) Problem 2 : The triangle ABC shown on the grid is the pre-image. Coordinates after dilation figure D In Exercises 710, the transformation of a figure into its image is described. (-4, 3) Section 10.1: Properties of Dilations. (-2, -2) ratio of y-coordinates = -4/-2 = 2, Question 2. endstream endobj 136 0 obj <>stream h24T0P044P06R 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 _______.