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1 2-1 Translations Use the figure below to answer Problems Triangle RST is translated along vector ν to create the image R'S'T'. What are the coordinates of the vertices of the image? R' S' T' 2. What is the length of vector ν? What is the length of RR? units units 3. If (x, y) is a point on RST, what is the corresponding point on R'S'T'? 4. Name vector ν using component form., 5. Name a pair of parallel segments formed by vertices of the preimage and the image. and Use the figure below to answer Problems Triangle J'K'L' is the image of JKL under a translation. Draw the translation vector ν from J to its image in J'K'L'. Write the vector in component form., 7. What is the slope of ν? _ 8. Triangle J'K'L' is also the image of DEF under a translation along a vector 6, 4. Find the coordinates of points D, E, and F, and draw DEF. D E F 22

2 2-2 Reflections Study the figures on the grid and answer the questions. 1. Which figure is the reflection of figure A over the y-axis? 2. Which two figures have x = 3 as their line of reflection? and 3. Which figure is the reflection of figure A over the line y = x? 4. What is the equation of the line of reflection for figures G and H? 5. Which figures are not reflections of Use principles of reflections to determine where to place the puck. figure A? Name all. _ Mike is playing air hockey and wants to bounce the puck off the wall and into the goal at G(3, 10). 6. If the puck is at P (2, 3), what point on the right wall (x = 6) should he aim for? Sketch and label a figure on the grid. Explain your answer. 7. If the puck is at (0, 4), what point on the wall should he aim for? 8. If the puck is at (3, 2), what point on the wall should he aim for? 9. If the puck is at (3, 6), what point on the wall should he aim for? 27

3 2-3 Rotations Follow the directions for Problems 1 5 to analyze rotations. 1. Draw a line from the origin, O, to point D and from O to D'. Measure the angle formed by OD and OD '. How many degrees was figure ABCD rotated? degrees 2. Find the coordinates of points on ABCD and corresponding points on its image. Label A', B', and C'. A(, ) B(, ) C(, ) D(, ) A'(, ) B'(, ) C'(, ) D'(, ) P(x, y) P'(, ) 3. If you rotate A'B'C'D' counterclockwise 90, what is the sign of the x-coordinates of the new image? Of the y-coordinates? In what quadrant is the new image? 4. Draw and label A''B''C''D'', the image of A'B'C'D' after being rotated 90 counterclockwise. 5. If (x, y) is a point on ABCD, what is its image on A''B''C''D''? (, ) Use principles of rotations to answer Problems What clockwise rotation produces the same image as a counterclockwise rotation of 220? clockwise 7. Tony Hawk was the first skateboarder to do a 900, a rotation of 900. How many times did he rotate on the skateboard? times 8. Each arm of this pinwheel is the image of another arm rotated around the center. What is the angle of rotation between one arm and the next? 32

4 2-4 Investigating Symmetry Use the figures on the grid to answer Problems What are the equations of the lines of symmetry for figure A? 2. Does figure B have line symmetry, rotational symmetry, or both? 3. If you rotate figure C all the way around point (7, 4), 50 at a time, will you create a figure with rotational symmetry? Explain your answer. Tell whether each figure appears to have line symmetry, rotational symmetry, both, or neither. If line symmetry, tell how many lines of symmetry. If rotational symmetry, give the angle of rotational symmetry Use principles of symmetry to answer Problems How many lines of symmetry does each quadrilateral have? isosceles trapezoid rectangle with sides square rhombus parallelogram with sides and angles How many lines of symmetry does a regular pentagon have? How many lines of symmetry does a regular hexagon have? 37

5 2-4 Investigating Symmetry Practice and Problem Solving: Modified A pentomino is a figure made by joining five congruent squares side to side. For Problems 1 6, identify the symmetry of each pentomino. If it helps, draw the pentomino on graph paper and cut it out. Experiment with folding to see if it has lines of symmetry. Rotate it to see if a rotation maps to the original figure. The first one is done for you. 1. Does it have line symmetry? Yes. 2. Does it have line symmetry? 3. Does it have line symmetry? 4. Does it have line symmetry? 5. Which of the pentominoes below is the only one that has rotational symmetry? A B C D 6. Which two pentominoes below have both line symmetry and rotational symmetry? and A B C D For each figure, draw all lines of symmetry and tell if it has rotational symmetry. The first one is done for you. 7. Yes