11-4 Translations and Reflections on the Coordinate Plane
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1 1. Triangle MNP is shown on the coordinate plane. Find the coordinates of the vertices of the image of the triangle MNP translated 5 units to the right and 3 units up. 4. Find the coordinates of the vertices of the image of XYZ translated 2 units to the left and 3 units up. X ( 2, 7), Y ( 4, 3), Z (0, 3) 5. The vertices of FGH are F( 3, 4), G(0, 5), and H (3, 2). Graph the triangle and its image after a reflection over the y-axis. M (1, 3), N (3, 4), P (1, 7) 2. The vertices of LMN are L(2, 1), M(5, 2), and N( 1, 4). Graph the triangle and its image after a reflection over the x-axis. 6. The vertices of figure RSTV are R(2, 4), S(4, 3), T(4, 2), and V(1, 2). Graph the figure and its image after a reflection over the y-axis. For Exercises 3 and 4, use the coordinate plane below. Triangle XYZ is shown. 3. Find the coordinates of the vertices of the image of XYZ translated 4 units to the right and 5 units down. X (4, 1), Y (2, 5), Z (6, 5) esolutions Manual - Powered by Cognero Page 1
2 7. The vertices of figure ABCD are A( 3, 1), B( 5, 1), C( 5, 6), and D( 3, 3). Graph the figure and its image after a reflection over the x-axis. 9. In chess, the rook can only move vertically or horizontally across the board. The chessboard below shows the movement of a rook after two turns. Describe this translation in words. 5 units left and 3 units up 8. Reflect the figure below over the x-axis. Sketch the figure and its image on grid paper. What is the animal? For Exercises 10 14, identify each transformation as a translation or a reflection and describe the transformation. For Exercises 10 12, the green image is the original. 10. translation; 5 units to the right. 11. a turtle reflection over the x-axis esolutions Manual - Powered by Cognero Page 2
3 A mosaic is a type of art created using glass, stone, tile, or other materials. Describe the transformation that maps the red outlined tile to the purple outlined tile. Translation; 5 units to the left and 4 units down 13. A figure has vertices H(1, 1), J(1, 5), K(3, 1), and L(3, 5). The image s vertices are H ( 4, 5), J ( 4, 1), K ( 2, 5), and L ( 2, 1). It is a translation 5 units left and 4 units down. 14. Triangle QRS has vertices Q(1, 1), R(5, 3), and S (3, 2). The vertices of the image are Q (1, 1), R (5, 3), and S (3, 2). It is a reflection over the x-axis. 15. Triangle RST has vertices R(4, 2), S( 8, 0), and T(6, 7). When translated, R has coordinates ( 2, 4). Find the coordinates of S and T. Then describe the translation of triangle RST onto triangle R S T. S'( 14, 2), T'(0, 9); The translation is to the left 6 units and up 2 units. a translation 1 unit right and 1 unit up 17. Model with Mathematics When using a rubber stamp, the image the ink makes on a page is a reflection of the stamp. Suppose you create a stamp that would print the word MATH. Draw the stamp. Is the image a reflection over the x-axis or y-axis? ; y-axis 18. Use Math Tools Draw a figure on the coordinate plane. Then reflect the figure over the y-axis. Sample answer: esolutions Manual - Powered by Cognero Page 3
4 19. Justify Conclusions Suppose you reflect a figure over the x-axis and then you reflect the figure over the y-axis. Is there a single transformation using reflections or translations that maps the original figure to its finaly image? If so, name it. Explain your reasoning. No; for example, the vertices of ΔABC are A(1, 3), B (7, 3), and C(1, 6). After a reflection over the x-axis and a reflection over the y-axis, the image s vertices are A'( 1, 3), B'( 7, 3), and C'( 1, 6). No single reflection or translation maps ΔABC to ΔA'B'C'. 20. Which One Doesn't Belong? Without graphing, identify the pair of points that does not represent a reflection over the y-axis. Justify your reasoning. 23. Which of the following is a vertex of the figure shown below after a translation of 2 units right and 2 units up? A (5, 0) B (0, 2) C (2, 0) D (0, 5) The pair G( 3, 4) and G'( 3, 4) is a reflection over the x-axis; to reflect over the y-axis, multiply the x- coordinate by Persevere with Problems Discuss how an image compares to the original figure if you reflect a triangle in Quadrant I over the x-axis, then translate the image 4 units right and 3 units up. Determine if a single transformation can map the original figure to the final image. No single transformation is equivalent to the original two. The new figure is a reflection of the original but moved up and over to the right. 22. Building on the Essential Question A figure is translated by (2, 3) and then the image is translated by ( 2, 3). Without graphing, describe the final position of the figure. Explain your reasoning. The final position of the figure will be the original position. Translating a figure by (2, 3) and then by ( 2, 3) is the same as translating it by (0, 0). D 24. SHORT RESPONSE The coordinates of a triangle are A(0, 1), B( 2, 1), and C(3, 5). What are the coordinates of the triangle after it has been translated 3 units left and 4 units down? A'( 3, 5) B'( 5, 5) C'(0, 1) 25. Which of the following best represents a reflection over the vertical line segment in the center of the rectangle? F G H J H esolutions Manual - Powered by Cognero Page 4
5 26. SHORT RESPONSE What are the coordinates of the point ( 3, 5) after it has been reflected over the y-axis? (3, 5) Name the ordered pair for each point graphed below. 33. Translate the phrase three times as many cards as Neville has into an algebraic expression. 3n 34. Translate the sentence below into an equation. The sum of three times a number and five is 20. 3n + 5 = 20 Factor each expression. If the expression cannot be factored, write cannot be factored. Use algebra tiles if needed x A 28. C 29. G 30. K ( 4, 4) (1, 3) ( 3, 2) (3, 4) 31. In their first five games, the Jefferson Middle School basketball team scored 46, 52, 49, 53, and 45 points. What was their average number of points per game? 49 points 3(x + 9) x 8(5 + x) 37. 3x + 41 cannot be factored x (3x + 4) x cannot be factored x (3x + 4) 32. Financial Literacy The starting balance in a checking account was $50. What was the balance after a $100 deposit was made and checks were written for $25 and for $32? $7; esolutions Manual - Powered by Cognero Page 5
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6-3 Rotations. The coordinates are R (7, 8), S (7, 2), and T. esolutions Manual - Powered by Cognero Page 1
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