COORDINATE ALGEBRA UNIT 5: TRANSFORMATIONS IN THE COORDINATE PLANE. 1. On this coordinate plane, UVW has been transformed to form its image U''V''W''.
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1 1. On this coordinate plane, UVW has been transformed to form its image U''V''W''. 3.Graph the figure and its image under the given translation: EFG with vertices E (-2, -3), F (-3, -2), G (-1, -1) under the translation left three units and down two units. Which statement describes the sequence of transformations? A reflection across the y-axis, followed by a translation of 2 units to the left and 9 units down reflection across the x-axis, followed by a reflection across the y-axis C rotation of 180 about the origin, followed by a translation of 2 units to the right and 1 unit down D translation of 2 units to the right and 1 unit up, followed by a rotation of 180 about the origin 4.In the figure below, determine whether the third figure is a reflected image of the first figure. 2. In the figure below, a b Determine whether the third figure is a translation image of the first figure. a b a A Yes; it is one reflection after another with No; it is a reflection followed by a translation. C No; it is a reflection followed by a rotation. D No; it is one reflection after another with b A Yes; it is one reflection after another with No; it is a reflection followed by a translation. C No; it is a reflection followed by a rotation. D No; it is one reflection after another with
2 5. Graph the figure and its image under the given translation (x, y) (x + 2, y 2): Given XYZ with endpoints X (-2, -2), Y (-4, -4), Z (-3, -4) 7. In the diagram, the dashed figure is the image of the solid figure. Name the image of E. A A R Q C E D T 8. The vertices of a triangle are P ( 7, 4), Q ( 7, 8), and R (3, 3). Name the vertices of the image reflected in the line y = x. A P` (4, 7), Q` (8, 7), R` (3, -3) P` (4, -7), Q` (8, -7), R` (3, 3) C P` (-4, - 7), Q` (-8, -7), R` (-3, 3) D P` (-4, 7), Q` (-8, 7), R` (-3, -3) 6. Given and P ( 4, 3), what is (P)? A P (6, 2) P (2, 4) C P ( 6, 2) D P ( 3, 5) 9. Describe in words the transformation represented by the translation (x + 2, y 1). A 2 units to the right and 1 units down 1 units to the right and 2 units down C 2 units to the left and 1 units down D 2 units to the left and 1 units up 10. P ( 5, 8) by a translation (x + 3, y + 5) and the reflection in the line y = x. Find the coordinates of the original point P. A (5, 0) ( 5, 0) C (11, 10) D ( 11, 10)
3 11. Which graph shows a triangle and its reflection image in the x-axis? 13. Which transformation from solid-lined figure to dashed-lined figure is given by the translation (x 3, y + 3) 12. The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 angles. Find the angle of rotation about O that maps P to G. A C 210 D 270
4 14. Square CDE and its image after rotation, square 'C'D'E', are graphed on the coordinate plane below. 15. Find the image for the composite transformation of the upper right triangle for the translation (x - 8, y - 7) and reflection in the line x = -3. A Which of the following best describes the rotation using function notation? A C D C D
5 16. Name the type of symmetry for the figure. 18. Graph the image of the figure M (-3, -2), V (-2, 0), T (1, -4), Y (-4, -2) using the transformation given: rotation 90 counterclockwise about origin. A reflection rotation C rotation and reflection D no symmetry 17. If the figure has rotational symmetry, find the angle of rotation about the center that result in an image that matches the original figure. 19. How many lines of symmetry does the figure have? A C 210 D no symmetry A 7 lines of symmetry 14 lines of symmetry C 28 lines of symmetry D infinitely many lines of symmetry
6 20. Which of the following best describes a geometric dilation? 22. The transformation from triangle JKL to triangle J'K'L' is shown on the coordinate plane below. A A transformation that turns a figure around a point A transformation that slides a figure to a new location C A transformation that flips a figure across a line D A transformation that enlarges or reduces the size of a figure by a certain scale factor 21. Which of the following is the definition of a circle? A A figure without corners or sides A figure with parallel sides of equal length C The resulting figure when a round cone is cut obliquely by a plane D The set of all points that are the same distance from a point called the center Which of the following best describes the dilation using function notation? A ( ) C D
7 CONSTRUCTED RESPONSES For questions complete as directed by the teacher. 23. A square has the vertices A (1, 4), (4, 7), C (7, 4), and D (4, 1). 25. Use the concept of geometric translation to give a definition of parallel lines. A Use 1 transformation to bring the figure back onto itself so that it looks the same. Write this transformation symbolically. Use at least 2 different types of transformations (rotation, reflection, or translation) to bring the figure back onto itself. Write these transformations symbolically. 24. The graph below shows trapezoid ACD and its reflection across the x-axis, A''C'D'. How would you represent the reflection performed using function notation? Show all your work.
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