9 3 Rotations 9 4 Symmetry

Transcription

1 h 9: Transformations 9 1 Translations 9 Reflections 9 3 Rotations 9 Smmetr 9 1 Translations: Focused Learning Target: I will be able to Identif Isometries. Find translation images of figures. Vocabular: Transformation Preimage Image Transformation: a change in the position, shape or size of a geometric figure. Eamples: Standard(s): Geometr.0. Students know the effect of rigid motions on figures in the coordinate plane and space, including translations. Isometr Rigid motion Translation The original figure (before the transformation) is the preimage. The resulting figure (after the transformation) is the image. Isometr: a transformation in which the preimage and image are congruent. An isometr can also be thought of as a rigid motion because lengths and angles are preserved. (same shape and size) Identifing Isometries: Does the transformation appear to be an a isometr? Eplain. I ll do one We ll do one together You tr A transformation maps a figure (preimage) onto its image and ma be described with arrow notation. Prime ( ) notation is sometimes used to identif image points. In the diagram below, K is the image of K K K' 1

2 Notice that ou name the corresponding parts of the preimage and the image in the same order, as ou do for corresponding points of congruent or similar figures. Naming Images and orresponding Parts: a. Name the images of and b. List all pairs of corresponding sides. We ll tr one: In the diagram, NID SUP. a. Name the images of J and point D b. List all pairs of corresponding sides. You tr: In the diagram, D E F is the image of DEF. a. Name the images of and F b. List all pairs of corresponding sides. Finding a translation image,, W Y Z-

3 We ll do one:,, 1 K J - L - You tr:, 5, 3 M N P - O -6 Writing a rule to describe a Translation: Write a rule to describe the translation PQRS P Q R S. We ll do one: You tr: 3

4 9 Reflections: Focused Learning Target: I will be able to Find reflection images of figures Vocabular: reflection Standard(s): Geometr.0. Students know the effect of rigid motions on figures in the coordinate plane and space, including reflections. Reflection (flip): an isometr in which a figure and its image have opposite orientations. It is the same as a mirror image. Eample: To reflect a figure across a line, use the following rules: If point A is on the line, then the image of A is itself. (A = A ). If point is not on the line, then the line is the perpendicular bisector of '. ( and are the same distance from the line, but on opposite sides). Eample: Finding Reflection images: Find the image of points P, Q and R reflected across the line = Q R - - P - -

5 We ll do one together: Find the image of points P, Q and R reflected across the ais P - R Q You Tr: Find the image of points A, & reflected about the line = A - Drawing reflection images: Given points A(3,), (0,1) & (,3), draw A and it s reflection image across the ais. We ll do one together: Given points J(1,), A(3,5) & R(,1), draw it s reflection image across the line = JAR and You Tr: Given points A(3,), (0,1) & (,1), draw it s reflection image across the ais A and 5

6 9 3 Rotations: Focused Learning Target: I will be able to draw and identif rotation images of figures Vocabular: rotation Standard(s): Geometr.0. Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations. center of rotation center of a regular polgon Rotation: a rotation is the action performed when an object is spun around a specific point. The point used to spin the object is the center of rotation. The center of rotation can be located on, or off the object. In addition, the rotation can be full 360, or partial. Eamples: When rotating an image about the origin, in multiples of 90, the resulting image is found b: lockwise: switching the values of and and negating the resulting coordinate for each 90 turn. (a rotation of 180 would use switches, a rotation of 70 would use 3 switches, etc.) ounter clockwise: switching the values of and and negating the resulting coordinate for each 90 turn. (a rotation of 180 would use switches, a rotation of 70 would use 3 switches, etc.) Alternative methods: (For both clockwise and counterclockwise) switch the values of and as stated above, but determine the signs based upon the quadrant the image is in. 90 o clockwise or 70 o counter clockwise (, ) (, ) 90 o counter clockwise or 70 o clockwise (, ) (, ) 180 o (for both clockwise or counter clockwise) (, ) (, ) Drawing a Rotation Image about the origin: Draw the image of A for a 90 rotation clockwise about the origin. A

7 We ll do one together: Draw the image of A for a 70 counterclockwise rotation about (0, 0) A You Tr: Draw the image of the origin. A for a 180 rotation about A - Identifing a rotational Image: What point represents a 7º clockwise rotation of point? E We ll do one together: What point represents a 135º clockwise rotation of point? A D A D H E G F You tr: What point represents a 0 o clockwise rotation of point? A D F E 7

8 9 Smmetr Focused Learning Target: I will be able to identif the tpe of smmetr in a figure Vocabular: Line smmetr Smmetr Rotational smmetr Reflectional smmetr Point smmetr There are two tpes of smmetr: Reflectional smmetr the figure has a line of smmetr that bisects the figure creating a mirror image (imagine folding a figure along a line so that both halves match perfectl). Rotational smmetr the figure can be rotated around its center b 180 o or less and still be in the eact same position. Identifing Reflectional Smmetr: Is it possible to have more than one line of smmetr? We ll do one together: You tr: Identifing Rotational Smmetr: Does each object have rotational smmetr? If so, give the angle(s) of rotation. We ll do one together: You tr: Does each object above have reflectional smmetr? If so, draw in the lines of smmetr. Group work: Using onl capital letters, which ones have reflectional smmetr? Which capital letters have rotational smmetr and b how man degrees? EX. The letter H has lines of smmetr and a rotational smmetr of 180 o 8

9 9 5 Dilations Focused Learning Target: I will be able to locate and find the dimensions and dilation images of figures. Vocabular: Reduction Dilation Similarit Enlargement Scale Factor A dilation is a transformation whose preimage and image are similar (i.e. figures that maintain the definitions of similarit). Enlargement the dilation is an enlargement if the scale factor is greater than 1. Reduction the dilation is an enlargement if the scale factor is between 0 and 1. Identifing Enlargement dilations: Question: We ll do one together: You tr: 9

10 Identifing Reduction Dilations: Question: We ll do one together: You tr: Question: Is it possible to dilate a 3 dimensional figure/object? 1) ) 10