Rotations: Day 3 Rotations.notebook. September 16, the center point of rotation (origin) 3. angle of rotation (multiples of 90) 0 o

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1 a 3 Rotations.notebook ROTTIONs rotation (turn) moves a figure around a point. This point is called the center of rotation. P Rotations: 1. direction (clockwise or counter clockwise) When ou rotate a figure, ou can describe the rotation b giving the direction (clockwise or counterclockwise) and the angle that the figure is rotated around the point of rotation. Rotations are counterclockwise unless ou are told otherwise. escribe each of the rotations. 2. the center point of rotation (origin) 3. angle of rotation (multiples of 90) This figure is rotated 90 degrees counterclockwise about point. This figure is rotated 180 degrees clockwise about point. ommon ngles of Rotation: counter clockwise 90 o 360 o 0 o clockwise 270 o (or 90 clockwise) Now let's look at the same figure and see what happens to the coordinates when we rotate a figure. Write the coordinates for the pre image and image. What do ou notice? ' ' ' ' On graph paper. oordinates in notebook. ( 4, 6) ' ( 6, 4) ( 1, 6) ' ( 6, 1) ( 2, 2) ' ( 2, 2) ( 5, 2) ' ( 2, 5) 180 o When rotated counter clockwise, the coordinate is the opposite of the pre image coordinate and the coordinate is the same as the pre image of the coordinate. In other words: (, ) (, ) 1

2 a 3 Rotations.notebook What happens to the coordinates in a half turn? an ou summarize what happens to the coordinates during a rotation? Write the coordinates for the pre image and image. ' ' 180 o ounterclockwise: (, ) (, ) Half turn: (, ) (, ) What do ou notice? ' ' 270 o ounterclockwise: (, ) (, ) ( 7, 5) ' (7, 5) ( 1, 5) ' (1, 5) ( 2, 1) ' (2, 1) ( 6, 1) ' (6, 1) When rotated a half turn, the coordinate is the opposite of the pre image coordinate and the coordinate is the opposite of the pre image of the coordinate. In other words: (, ) (, ) Tr: (2, 4) Rotate 180 ( 2, 4) Tr: ( 2, 4) Rotate 90 (4, 2) ( 1, 3) (4, 1) Rotate 90 Rotate 270 ( 3, 1) ( 1, 4) E (1, 3) F ( 5, 2) Rotate 270 Rotate 180 E ( 3, 1) F (5, 2) Name the coordinates of the point after the described rotation. E 1. (4, 5) 270 E 2. ( 3, 2) quarter turn clockwise a. ( 4, 5) b. ( 5, 4) c. (5, 4) d. ( 5, 4) a. (3, 2) b. ( 2, 3) c. (2, 3) d. ( 2, 3) 2

3 a 3 Rotations.notebook E 3. (6, 4) half turn a. ( 6, 4) b. ( 6, 4) c. ( 4, 6) d. (4, 6) E 4. ( 8, 2) 180 a. (8, 2) b. ( 8, 2) c. (2, 8) d. ( 2, 8) E 5. E (4, 2) 90 a. ( 4, 2) b. ( 4, 2) c. ( 2, 4) d. (2, 4) On white boards. 1. Plot and label the following 4 points on the coordinate grid: (2,2) (6, 2) (7,5) (3,5) 2. onnect the points to form a polgon. What is the best name for the figure formed? 3. Rotate the figure 270 and write the new coordinates. 4. Write a congruence statement

4 a 3 Rotations.notebook (2, 2) (2, 6) (5, 7) (5, 3) Rotate the figure 90 O counterclockwise around the origin corresponds to, so corresponds to, so Rotate the original figure 180 O clockwise about the origin corresponds to, so corresponds to, so Which lines are parallel? angle of rotation center of rotation F' (2, 1) (5, 1) (2, 2) (1, 2) ( 2, 1) (1, 5) ( 5, 1) ( 2, 2) ( 2, 2) F counter clockwise escribe the rotation shown: blue How is this figure rotated about the origin? In a coordinate plane, each quadrant represents ' ' ' ' L In order to determine the angle, draw two ras (one from the point of rotation to pre image point, the other from the point of rotation to the image point). Measure this angle. This shows a 270 (counter clockwise) rotation or a 90 o clockwise rotation of the blue figure about the origin. This figure is rotated 270 degrees clockwise about the origin or 90 degrees counterclockwise about the origin. heck to see if the pre image and image are congruent. 4

5 a 3 Rotations.notebook How man degrees and in which direction was each of the following rotated? The following descriptions describe the same rotation. What do ou notice? The sum of the two rotations (clockwise and counterclockwise) is 360 degrees. If ou have one rotation, ou can calculate the other b subtracting from

6 a 3 Rotations.notebook escribe each rotation in another wa clockwise 280 ounter clockwise counter clockwise 320 clockwise counter clockwise 125 clockwise 65 clockwise 295 counter clockwise 150 clockwise 210 counter clockwise Triangle is shown: What are the coordinates of the image of after a rotation of 90 o counterclockwise around the origin? X ' ' Rotational Smmetr Which figure(s) have rotational smmetr? Rotational Smmetr: a figure in a plane is said to have rotational smmetr if an image matches the original figure after a rotation of 180º or less Eample: oes this show rotational smmetr? 6