Name: Period 2/3/2012 2/16/2012 PreP UNIT 11: TRNSFORMTIONS I can define, identify and illustrate the following terms: Symmetry Line of Symmetry Rotational Symmetry Translation Symmetry Isometry Pre-Image Image Reflection Translation Rotation Composition of Transformations Glide Reflection Dilation Center of dilation Scale Factor Enlargement Reduction Tessellation Friday, 2/3 6 Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday lock Day Friday 3 1/2 1-7 and 12-1 Introduction and Reflections 12-2 and 12-3 Translations and Rotations 13 12-4 and 12 5 Compositions and Symmetry 1-7 asics and 12-1: Reflections 7 14 Quiz nd Functions 12 7 Dilations 8/9 D Functions Self Study 15/16 Review ND TEST 11 10 D Functions Self Study 17 End of 6 weeks Tessellations I can name the pre-image and image points of a transformation. I can identify reflections, rotations, and translations. I can use arrow notation to describe transformations. I can reflect across the x-axis, the y-axis, the line y = x, the line y = x or any given line. PRCTICE: pg. 53 #1-4, 7-9, 12-15, 19-22, 29-32; pg 827 #13-16, 20-23, 46-48 Monday, 2/6 12-2: Translations & 12-3: Rotations I can translate figures on the coordinate plane. I can change translation notation from vector notation a, b to coordinate notation (x, y) (x + a, y + b) and back again. I can rotate 90, 180, and 270 around the origin. I can determine the angle of rotation. PRCTICE: pg 834 #11-14, 17-20, 29-33, 39-40; pg 842 #12-15, 18-21, 27-30, 37, 40, 44 Tuesday, 2/7 QUIZ: Translations, Rotations, and Reflections Transforming Functions I can translate linear and quadratic functions along a vector. I can reflect linear and quadratic functions across the x-axis, y-axis, y = x or y = x. I can write the equation of a function after transformation. PRCTICE: Function Transformations Self-study packet
Wednesday, 2/8 or Thursday, 2/9 ND Friday, 2/10 D I can translate linear and quadratic functions along a vector. I can reflect linear and quadratic functions across the x-axis, y-axis, y = x or y = x. I can write the equation of a function after transformation. PRCTICE: Function Transformations Self-study packet Monday, 2/13 12-4: Compositions & 12-5: Symmetry I can perform a composition of two or more transformations. I can identify line symmetry, rotational symmetry and translation symmetry. I can draw a line of symmetry for a given figure. I can find the equation of a line of symmetry. PRCTICE: pg 851 #10, 14, 17-19, 23-25; Symmetry Worksheet Tuesday, 2/1/11 12-7: Dilations I can determine the scale factor of a dilation. I can create a dilation given a scale factor and center on a graph. I can determine the scale factor of an incomplete dilation and complete the dilation. PRCTICE: Dilations Worksheet Wednesday, 2/2/11 or Thursday, 2/3/11 REVIEW and then Test 11: Transformations Score: I can transform figures and functions. PRCTICE: Review Worksheet
Reflections Notes and Examples Isometry - Image - Preimage Mapping - (x, y) (x+2, y + 2) or C C Writing equations of and graphing horizontal and vertical lines. 1. This is the line y = 2. 2. This is the line x = 2. Which axis does it cross? Which axis does it cross? Where does it cross? Where does it cross? reflection is a transformation across a line so that the line of reflection is the perpendicular bisector of the segment joining each point and its image. 3. Reflect across x = 2 4. Reflect across y-axis 5. Reflect across x-axis D C C T T M H C M C D T T H 6. Reflect across y = x 7. Reflect across y = 3 8. Reflect across y = x H E V F I T M O H S F I H M O S H T V E Can you see a rule for each reflection?
Translations Ex: Write a translation statement for the following transformation and name the image: Translate the point (4, -5) to the left 2 and up 7. Translation Statement: Image: **This problem can also be written in vector notation. Move point along the vector <, >. Your Turn: 1. Write the translation statement and name the image: Translate R(3, 7) to the right 4 and up 3. Translation Statement: Image: 2. Write the translation statement and name the image: Translate U(-6, 3) along the vector < 2, -5> Translation Statement: Image: Example. Graph the translation of the Example: How could you show <2, -3> triangle along. What is the vector? on a graph? v lways rotate to the. Rotations 90 = turn, 180 = turns, 270 = turns, 360 = turns. Steps to Rotation: 1. Graph the pre-image. 2. Turn paper to the left. 3. WRITE DOWN coordinates of the image. 4. TURN PPER CK to the original position. 5. Graph the image.
Compositions composition of functions is one followed by. You use the of the first as the of the next. Ex. 1 Ex. 2 Graph Triangle C Graph Triangle C (2, 6) (7,3) C(3, -2) (2, 6) (7,3) C(3, -2) Reflect across x-axis Translate along <3,3> Rotate 90 Reflect across y = x C C C C Symmetry These figures have line symmetry; that is, they contain at least one line of symmetry that divides the figure into two congruent halves: Do these figures have a line of symmetry? If so, sketch it in. (There may be more than one!) 1. 2. 3. 4. 60 These figures have rotational symmetry. They can be rotated around a point by a certain number of degrees so that the image ends up to be exactly the same as the pre-image. The number of times the figure coincides with itself is the order of symmetry. Do the figures below have rotational symmetry? y how many degrees? What is the order of symmetry? 180 5. 6. 7. 8. Tell whether the figure with the given vertices has line symmetry and/or rotational symmetry. Give the angle if there is rotational symmetry. Draw the figure and any lines of symmetry. 9. ( 2, 2) (2, 2) 10. R( 3, 3) S(3, 3) C(1, 2), D( 1, 2) T(3, 3) U( 3, 3)
For each figure find (one of) the line(s) of symmetry. Write the equation of the line of symmetry. 11. 12. 13. Equation: Equation: Equation: 14. Rectangle LOVE 15. Isosceles Triangle PIG 16. Trapezoid TIME L(-4, 4) O(-2, 8) V(6, 4) E(4, 0) P(-8, -5) I(-5, 0) G(-2. -5) T(8, -7) I(5. -4) M(5, 0) E(8,3) Equation: Equation: Equation: 17. 18. 19. Equation: Equation: Equation:
Name: Period: GH Dilations dilation is a transformation that changes the of a figure but not its. The tells how much the figure is (gets bigger) or (gets smaller). To dilate a figure, each point by the. The of dilation is the intersection of all the lines that connect every point with its image. Ex: Dilate (-2, 2) (2, 2) C(1, -2) D(-1, -2) by a scale factor of 3. C D Ex: Dilate (-2, 2) (2, 2) C(1, -2) D(-1, -2) by a scale factor of 1/2. C D The scale factor is found by writing a ratio of over. (or new over old) If the absolute value of the scale factor is then you have an enlargement, if it is between 0 and 1 you have a, and if it is 1 there is no change. Ex. 4 scale factor = 2 Ex. 5 scale factor = 3 2 Ex. 6 Ex. 7 Ex. 8 5 in. 3 in. 2.5 ft.75 ft 12 cm 6 cm Ex. 10 The graph shows C with vertices (-2, 2), (1, 3), and C (1, -1) and SU with endpoints S (-4, 4) and U (2, 6). t what coordinates would vertex T be placed to create STU, a triangle that is a dilation of C? F (-2, 2) G (2, -2) H (3, -3) J (.5, -.5) S U C
Practice 1-3: Tell whether each picture appears to be a dilation. 1) 2) 3) 4) scale factor = 3 5) scale factor = 2 (-4, 4) (2, 4) C(-2, -2) C 6)scale factor = 3 2 E(-4,-4) (-4,0) R(0,4) T(4,0) H(4, -4) 7) scale factor = 2 3 W(0,-3) O(-3,6) R(6,6) K(3,-3) E R T H W O R K 8) The graph shows PQR with vertices P (2, 4), Q (8, 6), and R (6, 2) and SU with endpoints S (5, 10) and U (15, 5). t what coordinates would vertex T be placed to create STU, a triangle that is a dilation of PQR? S F (12, 9) G (16, 12) H (20, 15) J (24, 18) P R Q U
Name: Period: GH Review 1. Graph the translation of the triangle along. What is the vector? 6. For each figure find the line of symmetry. Write the equation of the line of symmetry. v 2. Translate the function along the given vector. Write the equation of the new line. y = 2x + 3 along 2, 4 7. Which transformation(s) are always isometry transformations? Why? 8. What is preserved in an isometry transformation? What is not(hint: think reflections and rotations)? 9. For each transformation, determine which type it is ND the specific rule used. 3. Triangle C has vertices (-2, 4), (2, -3), and C(7, 1). Under a translation,, the image point of, is located at (-5, 2). Under this same translation, point C is located where? 4. MJR has vertices M(c, s), J(e, p), and R(a, t). What will be the new coordinate of point R if the triangle is translated 3 units to the left and 10 units up? 5. Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of symmetry. Then tell whether the figure has line symmetry. If so, draw in the lines of symmetry. 10.Describe the pattern shown in the figures below?
11. Reflect the given function or image across the given line of reflection. 2 y = x + 2 ; x-axis y = 2x + 4 ; y = x 15. 2004 Summer Exit If quadrilateral STUV is rotated 180 around the origin, in which quadrant will point S appear? C D Quadrant I Quadrant II Quadrant III Quadrant IV Equation: Equation: Reflect across 3 y = H T 16. The graph shows C with vertices (-2, 2), (1, 3), and C (1, -1) and SU with endpoints S (-4, 4) and U (2, 6). t what coordinates would vertex T be placed to create STU, a triangle that is a dilation of C? F (-2, 2) U G (2, -2) S H (3, -3) J (.5, -.5) C 12. Rotate the figures by the amount given. Write a rule for them. 13. What is the rule for the composite transformation formed by a translation of 4 units to the left and 3 units up, followed by a 90 counterclockwise rotation? 17. 2006 10 th Grade Pentagon PQRST is graphed on the coordinate grid below. Which of the following points would be the location of S if pentagon PQRST is dilated by a scale factor of 2 and has a center of dilation at (0, 0)? F ( 6, 4) G (2, 6) H (4, 6) J (4, 3) (x, y) (, ) 14. Point W is the image of point W after a counterclockwise rotation of 180 about the origin. If the coordinates of W are (-3, 8), what are the coordinate of W? 18. How do you find the center of dilation? 19. How do you find the scale factor?