UNIT 5: Transformations

Size: px

Start display at page:

Download "UNIT 5: Transformations"

Byron Matthews
6 years ago
Views:

1 Period: Date: May 11 & 12, 2015 UNIT 5: Transformations Checklist MAX Scored 1 Vocabulary 40 2 Transformations 30 3 Constructions 20 4 Random Transformations 30 Totals 120 Semester 2 Test Prep

2 Section 1. Vocabulary Word Bank (word is used only once; not all words will be used below) Dilation Reflection Stretch / Shrink Enlarges Rotation Translation Isometric Transformation Shrinks Transformation Df R30 rx-axis Th,k A is an operation that maps or moves the points of a figure in a plane. An is a transformation that keeps the size and shape of the figure identical or congruent. We examined three type of isometric transformations. A moves, shifts or slides the figure in the coordinate plane. A provides a mirror image of the figure by flipping the figure against designated line. A turns the figure about a fixed point. Other types of transformations we ve examined are not isometric: A uses a scalar multiple to enlarge or shrink the figure. These transformations are denoted by the form, with F being the multiplicative factor. If F > 1, the image is ; if F < 1, the image. Of note, a dilation changes the lengths of a shape, but retains congruent angles. 2 Semester 2 Test Prep

3 A multiplies the planar coordinates by different scalar factors. These transformations are denoted by the form S a,b with a being the x multiplier and b being the y multiplier. Of note, if a 1 and b 1, the image will have no congruent sides or angles. 1 When working with multiple transformation, order matters. If you change the order of the multiple transformations, you will typically get a different image. 2 When working with multiple transformations, you work the order insideout, meaning you start with the most inner transformation, then work toward the outside. 3 T h,k (R 90(x,y)) = R 90 (T h,k (x,y)) 4 R 180 (x,y) = r x=y (r x=-y(x,y)) T F Fill in the transformation mappings: Translation Reflection Rotation Th,k = (x+h, y+k) rx-axis (x,y) = (, ) ry-axis (x,y) = (, ) rx=y (x,y) = (, ) The rotations about the origin (0,0): R90 (x,y) = (, ) R180 (x,y) = (, ) R270 (x,y) = (, ) 3 Semester 2 Test Prep

4 Match the definition to the key word. a. Point b. Rhombus c. Angle d. Line Segment e. A rectangle f. Midpoint A. Identical in form and measurement B. A set of collinear points with two reference points. C. Lines that have equal slopes but different y-intercepts. D. A set of points which are all the same distance from a certain point. E. An exact position or location in a plane. F. An angle that measures exactly 90 G. Part of a line with two end points g. Circle h. Right Angle i. Congruent j. Line k. A square l. Perpendicular Lines m. Parallel Lines H. A figure formed by two rays with a common endpoint I. Lines that have slopes that are opposite sign reciprocals J. A parallelogram with 4 congruent sides. K. A parallelogram with 4 right angles L. A parallelogram with 4 right angles AND 4 congruent sides M. A line that cuts across two or more parallel lines N. The point that divides a line segment into exactly two equal parts n. Transversal line 4 Semester 2 Test Prep

5 Section 2. Transformations A. T3,-3 (7,3) = B. rx-axis (-8,5) = C. T2,3 (R180 (-5,2)) = D. R180 (T2,3 (-5,2)) = E. rx=y (R270 (-3,-4)) = F. D4 (-5,3) = G. R90 (-3,-5) = H. r x=1 (4,-2) = I. r y=-1 (2,18) = J. r x=-y (-4, 1) = K. If g(x,y) = (5, -8) and f(x,y) = (2x+1, -3y-2), then f(g(x,y)) = L. If A = (-3,9), then rx-axis (R180 (A)) = M. Given P(-3,6) and T(x-4,y+2), P after a reflection over the y-axis of the point T(P).... N. What is point A if A(-3,7) has undergone r ( x axis ) (T 7, 2 (A))? 5 Semester 2 Test Prep

6 Section 3. Constructions A. Draw an image with one line of symmetry. B. Draw an image with three lines of symmetry. C. Draw an image with an infinite number of lines of symmetry. D. 6 Semester 2 Test Prep

7 E. Which of the following is the definition of a circle? a) A figure without any corners b) A figure with an infinite number of parallel lines of equal length c) The resulting figure when a rounded cone is cut obliquely (look up the word) by a plane. d) The set of all points that are the same distance from a point called a center. F. Describe every transformation that maps a square with points (2,2), (-2,2), (-2,-2) and (2,-2) onto itself. Hint: there are at least 5 transformations. G. Hint: Start with the graph 7 Semester 2 Test Prep

8 Section 4. Random Transformations A. Find the coordinates of the vertices of R 180 (T -3,8 ( ABC) where A (2,3), B (6,7) and C (9,4). Hint: Use a table!!!!!!!! B. Given the figure below, ABC, what would be the coordinates under R180 (T3,-2 ( ABC) Hint: Use a table or a graph! Initial A (1,4) B (6,3) C (3,1) C. 8 Semester 2 Test Prep

9 D. E. 9 Semester 2 Test Prep

10 F. G. 10 Semester 2 Test Prep

11 H. I. 11 Semester 2 Test Prep

12 J. K. 12 Semester 2 Test Prep

13 KEY 13 Semester 2 Test Prep

14 Section 1. Vocabulary (One point each response) KEY A TRANSFORMATION is an operation that maps or moves the points of a figure in a plane. An ISOMETRIC TRANSFORMATION is a transformation that keeps the size and shape of the figure identical or congruent. We examined three type of isometric transformations. TRANSLATION A moves, shifts or slides the figure in the coordinate plane. A REFLECTION provides a mirror image of the figure by flipping the figure against designated line. A ROTATION turns the figure about a fixed point. Other types of transformations we ve examined are not isometric: A DILATION uses a scalar multiple to enlarge or shrink the figure. These transformations are denoted by the form, with F being the multiplicative factor. If F > 1, the image is ; ENLARGED if F < 1, the image. SHRINKS D F Of note, a dilation changes the lengths of a shape, but retains congruent angles. A STRETCH / SHRINK multiplies the planar coordinates by different scalar factors. These transformations are denoted by the form S a,b with a being the x multiplier and b being the y multiplier. Of note, if a 1 and b 1, the image will have no congruent sides or angles. 14 Semester 2 Test Prep

15 1 When working with multiple transformation, order matters. If you change the order of the multiple transformations, you will typically get a different image. 2 When working with multiple transformations, you work the order insideout, meaning you start with the most inner transformation, then work toward the outside. T T T F 3 T h,k (R 90(x,y)) = R 90 (T h,k (x,y)). Order matters. F 4 R 180 (x,y) = r x=y (r x=-y(x,y)) T Translation Reflection Rotation T h,k = (x+h, y+k) r x-axis (x,y) = ( x, -y ) r y-axis (x,y) = ( -x, y ) r x=y (x,y) = ( y, x ) R 90 (x,y) = ( -y, x ) R 180 (x,y) = ( -x, -y ) R 270 (x,y) = ( y, -x ) 15 Semester 2 Test Prep

16 a. E Point b. J Rhombus c. H Angle d. G Line Segment e. K A rectangle f. N Midpoint A. Identical in form and measurement B. A set of collinear points with two reference points. C. Lines that have equal slopes but different y-intercepts. D. A set of points which are all the same distance from a certain point. E. An exact position or location in a plane. F. An angle that measures exactly 90 G. Part of a line with two end points g. D Circle h. F Right Angle i. A Congruent j. B Line k. L A square l. I Perpendicular Lines m. C Parallel Lines H. A figure formed by two rays with a common endpoint I. Lines that have slopes that are opposite sign reciprocals J. A parallelogram with 4 congruent sides. K. A parallelogram with 4 right angles L. A parallelogram with 4 right angles AND 4 congruent sides M. A line that cuts across two or more parallel lines N. The point that divides a line segment into exactly two equal parts n. M Transversal 16 Semester 2 Test Prep

17 Section 2. Transformations (One point each response) Translation: Reflections: Rotations: Dilation: Thk, ( x, y) ( x h, y k) rx axis ( x, y) ( x, y) R90( x, y) ( y, x) DF (x,y) = (Fx, Fy) r ( x, y) ( y, x) R ( x, y) ( x, y) y x r ( xy, ) ( x, y) y axis 180 R ( x, y) ( y, x) 270 A. T 3,-3 (7,3) = (10,0) B. r x-axis (-8,5) = (-8,-5) C. T 2,3 (R 180 (-5,2)) = (7,1) D. R 180 (T 2,3 (-5,2)) = (3,-5) E. r x=y (R 270 (-3,-4)) = (3,-4) F. D 4 (-5,3) = (-20, 12) G. R 90 (-3,-5) = (5,-3) H. r x=1 (4,-2) = (-2,-2)... draw diagram I. r y=-1 (2,18) = (2,-20)... draw diagram J. r x=-y (-4, 1) = (-1, 4)... draw diagram K. If g(x,y) = (5, -8) and f(x,y) = (2x+1, -3y-2), then f(g(x,y)) = (11,22) L. If A = (-3,9), then r x-axis (R 180 (A)) = (3, 9) M. Given P(-3,6) and T(x-4,y+2), P after a reflection over the y-axis of the point T(P).... P = (7,8) N. What is point A if A(-3,7) has undergone r ( x axis ) (T 7, 2 (A))? A = (4, -5). 17 Semester 2 Test Prep

18 Section 3: Constructions A. Draw an image with one line of symmetry. B. Draw an image with three lines of symmetry. Equilateral Triangle C. Draw an image with an infinite number of lines of symmetry. A circle D. a. A reflection about the line y = -1 A rotation of 360 about (2, -1) b. A reflection about y = 1 A reflection about x = -2 A rotation of 180 about (-2, 1) A rotation of 360 about (-2, 1) E. Definition of a circle: Answer: (d) 18 Semester 2 Test Prep

19 F. Transformations of a square onto itself: R90. Technically, any rotation that is a whole-number multiple of 90 0 works. r x-axis r y-axis r y = x r y = -x G. Transformation of a hexagon Mapping onto itself (minimums): Rotation R 60 (or whole number multiples of 60 ) rx-axis ry-axis ry=-1.73x ry=1.73x ry=-0.58x ry=0.58x 19 Semester 2 Test Prep

20 Section 4: Various transformations A. Find the coordinates of the vertices of R 270 (T -3,8 ( ABC) where A (2,3), B (6,7) and C (9,4). Initial T-3,8 R270 A (2,3) (-1,11) (11,1) B (6,7) (3,15) (15,-3) C (9,4) (6,12) (12,-6) B. Given the figure below, ABC, what would be the coordinates under R180 (T3,-2 ( ABC) Initial T3,-2 R180 A (1,4) (4,2) (-4,-2) B (6,3) (9,1) (-9,-1) C (3,1) (6,-1) (-6,1) C. 20 Semester 2 Test Prep

21 D. a. Rotate ABCD by R-90 on Point (0,0), then Translation: T0,-3 (note: R-90 R270) b. Reflection of ABCD on y = 1, then Translation: T6,0 E. Answer: Selection C. F. Answer: Selection B (a flip or reflection on the y-axis) G. Answer: Selection C. A: (x,y) (-x,y) (x,-y) (-x,-y). NO B: (x,y) (x,-y) (-x,-y) (-x,y). NO C. (x,y) (-x,y) (-x,-y) (x,y). YES D. (x,y) (x,-y) (-x,-y) (-y, x) NO H. Answer: Selection B. I. Answer: Selection C. A classic rotation of R270 (x,y) (y, -x) J. Answer: Selection A. Picking Point M (5,1) to M (-9,-1) A: (5,1) (-5,1) (-9,1) (-9,-1). YES B: (5,1) (-5,-1) (5,-1) (7,-1). NO C: (5,1) (1,1) (1,-1) (-1,-1). NO D: (5,1) (1, -5) (1, 5) (5, -1) K. Answer: Selection C. T12, Semester 2 Test Prep

Translations SLIDE. Example: If you want to move a figure 5 units to the left and 3 units up we would say (x, y) (x-5, y+3).

Translations SLIDE. Example: If you want to move a figure 5 units to the left and 3 units up we would say (x, y) (x-5, y+3). Translations SLIDE Every point in the shape must move In the same direction The same distance Example: If you want to move a figure 5 units to the left and 3 units up we would say (x, y) (x-5, y+3). Note: