Line Symmetry a figure has line symmetry if the figure can be mapped onto itself by a reflection over a line drawn through the figure.
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1 Geometry Unit 3 Transformations Test Review Packet Name: The Unit Test on Transformations contains the following topics: Isometries Translations Using Mapping Notation Using Vector Notation Naming Vectors, Component Form, Length of a Vector: a 2 + b 2 Reflections Over x-axis Over y-axis Over y = x Over y = -x Over vertical lines (x = ) Over horizontal lines (y = ) Rotations 90, 180, 270 about origin on coordinate plane Construct rotations using a ruler and protractor Composition of Transformations on the coordinate plane (does order matter?) Symmetry Line Symmetry a figure has line symmetry if the figure can be mapped onto itself by a reflection over a line drawn through the figure. Rotational Symmetry a figure has rotational symmetry if the figure can be mapped onto itself by a rotation of 180 or less about the center of the figure. Determining rotational symmetry: 360 # of lines of symmetry (and all multiples up to 180 ) Dilation a similarity transformation in which a figure is enlarged using a scale factor greater than one or reduced using a scale factor between zero and one. Graph a figure and its dilation on the coordinate plane Construct the dilation of a figure using a ruler
2 1. Use the translation (x, y) (x + 2, y 5): a. What is the image of D (4, 7)? b. What is the pre-image of M (-5, 3)? 2. The vertices of Δ MNO are M (-2, 4), N (-1, 1), and O (3, 3). Graph Δ MNO and its image using prime notation after the translation (x, y) (x + 4, y 2): M : N : O : 3. ΔR S T is the image of ΔRST after a translation. Write a rule for the translation in mapping notation and in vector notation. R T S R T S Mapping Notation: Vector Notation: 4. Name the vector, write its component form, and find its length: a. b. E T M V
3 5. Write the component form of the vector that describes the translation from S (-3, 2) to S (9, -7). 6. The vertices of ΔABC are A (0, 4), B (2, 1) and C (4, 3). Graph and label the coordinates of ΔA B C after each transformation. a. Translate ΔABC using the vector 3, 1. b. Reflect ΔABC over the x-axis. c. Reflect ΔABC over the line y = - x. d. Reflect ΔABC over the line y = The vertices of ΔABC are A (-3, 1), B (1, 1) and C (1, -2). Reflect ΔABC over the line x = 2. Then reflect ΔA B C over the line y = -3. Graph ΔABC, ΔA B C, and ΔA B C. State the coordinates of ΔA B C. A : B : C :
4 8. The coordinates of ABC are A (0, 4), B (3, 6), and C (5, 2). Graph ABC. Rotate ABC 90, 180, and 270 counterclockwise about the origin. Record the coordinates after each rotation. After a 90 Rotation: A B C After a 180 Rotation: A B C After a 270 Rotation: A B C 9. List the image of each of the following points after the specified composition of transformations: a. If point A (-2, 5) is reflected in the y-axis, and then point A is reflected in the x-axis, the coordinates of point A are. b. If point B (-4, -2) is reflected over the line y =- x, and then point B is rotated 90 counterclockwise about the origin, the coordinates of B are. c. If point C (6, -3) is reflected over the line y = x, and then point C is rotated 270 counterclockwise about the origin, the coordinates of C are. d. If point D (-2, 10) is rotated 180 about the origin, and then point D is reflected over the line y=-5, then the coordinates of D are. e. If point E (0, 2) is reflected over the x-axis, and then point E is translated using the vector 1, 2, then the coordinates of E are. 10. Point P (-6, 2) is transformed to point P (2, 6). What is the transformation that maps P into P? Explain.
5 11. Use a ruler and protractor to rotate RST 140 counterclockwise about point P. 12. The vertices of ABC are A (2, 4), B (7, 6) and C (5, 2). Graph the image of ABC after a composition of the transformations in the order they are listed. Transformation: (x, y) (x + 2, y 4) Rotation: 180 about the origin 13. Describe the composition of transformations from ABC to A B C. a. b.
6 14. State the number of lines of reflection and the angle(s) of rotational symmetry of each of the following figures: a. Rectangle b. Isosceles Triangle c. Square # of Lines: # of Lines: # of Lines: Angle(s): Angle(s): Angle(s): d. Regular Octagon e. Equilateral Triangle f. Parallelogram # of Lines: # of Lines: # of Lines: Angle(s): Angle(s): Angle(s): 15. Use a ruler to construct a dilation of ABC with center O and a scale factor of The coordinates of PQR are: P (4, 2), Q (-4, 4), R (0, -5). a. Draw the dilation of PQR centered at the origin with a scale factor of 2 b. Draw the dilation of PQR centered at the origin with a scale factor of ½
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