11-7 Dilations on the Coordinate Plane

Transcription

1 Find the vertices of each figure after a dilation with the given scale factor k. Then graph the image. 2. k = 1. k = 3. A square has vertices M(0, 0), N(3, 3), O(0, 6) and P( 3, 3). Find the coordinates of the square after a dilation with a scale factor of 2.5. M'(0, 0), N'(7.5, 7.5), O'(0, 15), P'( 7.5, 7.5) 4. Jorge is using a photocopier to reduce a poster that is 8 inches by 14 inches to 5 inches by inches. What is the scale factor of the dilation? 5. Karen uses grid paper to help her enlarge her painting from 14 inches by 22 inches to 35 inches by 55 inches. What is the scale factor of the dilation? 2.5 esolutions Manual - Powered by Cognero Page 1

2 Find the vertices of each figure after a dilation with the given scale factor k. Then graph the image. 6. k = 4 7. k = k = esolutions Manual - Powered by Cognero Page 2

3 9. k = 11. W(0, 0), X(5, 5), Y(5, 10); k = W (0, 0), X (2, 2), Y (2, 4) Find the vertices of each figure after a dilation with the given scale factor, k. Then graph the original image and the dilation. 10. G( 1, 1), H(2, 1), J(3, 2), K( 2, 2); k = 2 G ( 2, 2), H (4, 2), J (6, 4), K ( 4, 4) 12. R( 1, 2), S(1, 4), T(1, 1); k = 3 R ( 3, 6), S (3, 12), T (3, 3) esolutions Manual - Powered by Cognero Page 3

4 13. A( 3, 5), B(0, 2), C(3, 1), D(0, 4); k = 17. Quadrilateral A'B'C'D' is a dilation of quadrilateral ABCD. Find the scale factor of the dilation and classify it as an enlargement or a reduction. scale factor: ; reduction 14. In a microscope, the image of a 0.16-millimeter paramecium appears to be 32 millimeters long. What is the scale factor of the dilation? During an eye exam, an optometrist dilates her patient s pupils to 7 millimeters. If the diameter of the pupil before dilation was 4 millimeters, what is the scale factor of the dilation? 16. Be Precise Jung is editing a digital photograph that is 640 pixels wide and 480 pixels high on his computer monitor. a. If Jung zooms the image on his monitor 150%, what are the dimensions of the image? b. Suppose that Jung is going to use the photograph in a design and wants the image to be 32 pixels wide. What scale factor should he use? c. Jung resizes the photograph so it is 600 pixels high. What scale factor did he use? a. 960 pixels by 720 pixels 18. Triangle L'M'N' is a dilation of triangle LMN. Find the scale factor of the dilation and classify it as an enlargement or a reduction. scale factor: 1.5; enlargement 19. Felicia wants to project a 2-inch by 2-inch slide on to a wall to create an image 128 inches by 128 inches. If the slide projector makes the dimensions of the image twice as large for each yard that it is moved away from the wall, how far away should Felicia place the projector? 6 yd b. c esolutions Manual - Powered by Cognero Page 4

5 20. Use Math Tools Draw a triangle on grid paper. Then draw the image of the triangle after it is moved 5 units right and then dilated by a scale factor of. Sample answer: 22. Reason Inductively A triangle has coordinates A(0, 5), B(0, 0) and C(10, 5). Find the coordinates of the final image after each set of dilations. a. k = 2 followed by k = b. k = followed by k = 2 c. k = followed by k = 2 d. k = 2 followed by k = a. A'(0, 4), B'(0, 0), C'(8, 4) b. A'(0, 4), B'(0, 0), C'(8, 4) c. A'(0, 2.5), B'(0, 0), C'(5, 2.5) d. A'(0, 2.5), B'(0, 0), C'(5, 2.5) 21. Persevere with Problems Suppose a figure ABCD is dilated by a scale factor of and then reflected over the x-axis and the y-axis. The final image is shown on the graph below. Graph the original image and list the coordinates of points A, B, C, and D. 23. Reason Inductively Refer to Exercise 22. Does the order in which you perform multiple dilations always, sometimes, or never result in the same image? Explain. Always. Sample answer: In examples a-d, both sets of two dilations have the same image. 24. Which One Doesn't Belong? Which pair of points does not represent a dilation with center at the origin? Explain. Sample answer: A( 2 4), B( 6, 10), C( 10, 8), D ( 12, 4) C(2, 5), C (4, 7); Sample answer: Dilations involve multiplying the coordinates by the scale factor. In the points C(2, 5) and C (4, 7), 2 is added to each coordinate. 25. Building on the Essential Question A triangle has one vertex at point (3, 6). It is dilated with a center at the origin by a scale factor of 3. The resulting image is then dilated with a scale factor of. What are the coordinates of that vertex after both dilations? Explain your reasoning. (3, 6); Sample answer: Multiplying by 3 and then by is the same as multiplying by 1. When multiplied by 1, the point will remain the same. esolutions Manual - Powered by Cognero Page 5

6 26. Quadrilateral PQRS was dilated to form quadrilateral P'Q'R'S'. 28. Let G(6, 8) be a point on triangle FGH. What are the coordinates of G' if the triangle is dilated by a scale factor of? A (3, 4) B (3, 4) C ( 3, 4) D ( 3, 4) Which number best represents the scale factor used to dilate quadrilateral PQRS to quadrilateral P Q R S? A 2 B C D 2 B 29. Short Response Point P( 10, 5) is on rectangle PQRS. If the coordinates of P after a dilation are ( 4, 2), what is the scale factor of the dilation? Triangle RSK is similar to RUV. What is the value of x, rounded to the nearest tenth? C 27. A triangle has vertices (1, 1), ( 2, 6), and (4, 1). If the triangle undergoes a dilation with a scale factor of 3, what will be the vertices of the image? F (3, 3), ( 6, 18), (12, 3) G (3, 3), (6, 18), (12, 3) H (3, 3), ( 6, 18), (12, 3) J (3, 3), ( 6, 18), ( 12, 3) F 2.1 km On a map of South Carolina, the scale is 1 inch = 20 miles. Find the actual distance for each map distance mi mi esolutions Manual - Powered by Cognero Page 6

7 33. Financial Literacy The table below shows the exchange rates for certain countries compared to the U.S. dollar on a given day. a. What is the cost of an item in U.S. dollars if it costs in British pounds? b. Find the cost of an item in South African rand if it costs in U.S. dollars. Country Rate per $1 (U.S.) Great Britain pounds South Africa rand a. $31.23 b rand 34. Reason Abstractly Write a vocabulary term that completes the analogy. Slide is to translation as? is to reflection. flip 35. Identify the transformation below as a translation or a reflection. Then describe the transformation. A triangle has vertices A(2, 2), B(2, 10), and C(6, 2). The image s vertices are A'(0, 3), B'(0, 9), and C'(4, 3). The transformation is a translation. The triangle is translated left 2 units and down 1 unit. esolutions Manual - Powered by Cognero Page 7