Transformations: Rotations on a Coordinate Plane Meet TED. TED is going to help us learn about rotations.
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- Herbert Lawrence
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1 Meet TED. TED is going to help us learn about rotations. First let s focus on TED s eyes. What are the coordinates of his left eye? What are the coordinates of his right eye? Good, now you will need to use those coordinates in order to help you discover to rules for rotations. Before we go any further lets discuss the direction in which we rotate. Remember that our coordinate plane is broken into quadrants numbers 1 4. When we rotate we always go in order of quadrant unless told otherwise. II y I A full rotation is 360 so if you rotate halfway around that would be a rotation. A 90 rotation moves of the way around, which just means it moves one quadrant counter-clockwise. If you rotated a figure 90 from quadrant 4 it would then be in quadrant. Let s start with the easy one. What happens when TED rotates 180? III IV x What are the new coordinates of TED s left eye? (, ) What are the new coordinated of TED s right eye? (, ) Write a rule for a 180 rotation. (x, y) (, )
2 Now let s see what happens when we only rotate him 90. What are the new coordinates of TED s left eye? (, ) What are the new coordinated of TED s right eye? (, ) Write a rule for a 90 rotation. (x,y) (, ) A 270 is like doing a 90 rotation 3 times. This means we will go of the way around. What are the new coordinates of TED s left eye? (, ) What are the new coordinated of TED s right eye? (, ) Write a rule for a 270 rotation. (x,y) (, )
3 Independent Practice Directions: Tell where each point would end up if it rotated the given distance. Given Point 90 rotation 180 rotation 270 rotation ex (1, 7) (-7,1) (-1, -7) (7, -1) 1. (2, 9) 2. (3, -5) 3. (-8, 2) 4. (-5, -8) 5. (4, 4) 6. (3, 0) Directions: Rotate each figure the given distance. Sketch the new shape and label the points. Rotate the figure 180 Rotate the figure 90 Rotate the figure 270 Rotate the figure 180
4 Answer KEY Meet TED. TED is going to help us learn about rotations. First let s focus on TED s eyes. What are the coordinates of his left eye? (6, 5) Be careful here, a lot of students (as well as me the first time) mix up TED s left eye with their own left. What are the coordinates of his right eye? (4, 5) Good, now you will need to use those coordinates in order to help you discover to rules for rotations. Before we go any further lets discuss the direction in which we rotate. Remember that our coordinate plane is broken into quadrants numbers 1 4. When we rotate we always go in order of quadrant unless told otherwise. II y I A full rotation is 360 so if you rotate halfway around that would be a 180 rotation. A 90 rotation moves of the way around, which just means it moves one quadrant counter-clockwise. If you rotated a figure 90 from quadrant 4 it would then be in quadrant I. Let s start with the easy one. What happens when TED rotates 180? III IV x What are the new coordinates of TED s left eye? (-6,-5) What are the new coordinated of TED s right eye? (-4, -5) x and y changed to their opposites Write a rule for a 180 rotation. (x, y) (-x, -y)
5 Now let s see what happens when we only rotate him 90. What are the new coordinates of TED s left eye? (-5, 6) What are the new coordinated of TED s right eye? (-5, 4) y became x and changed to its opposite x became y Write a rule for a 90 rotation. (x, y) (-y, x) A 270 is like doing a 90 rotation 3 times. This means we will go of the way around. What are the new coordinates of TED s left eye? (5, -6) What are the new coordinated of TED s right eye? (5, -4) x became y and changed to its opposite y became x Write a rule for a 270 rotation. (x,y) (y, -x)
6 Independent Practice Directions: Tell where each point would end up if it rotated the given distance. Given Point 90 rotation 180 rotation 270 rotation ex (1, 7) (-7,1) (-1, -7) (7, -1) 1. (2, 9) (-9, 1) (-2, -9) (9, -2) 2. (3, -5) (5, 3) (-3, 5) (-5, -3) 3. (-8, 2) (-2, -8) (8, -2) (2, 8) 4. (-5, -8) (8, -5) (5, 8) (-8, 5) 5. (4, 4) (-4, 4) (-4, -4) (4, -4) 6. (3, 0) (0, 3) (-3, 0) (0, -3) Directions: Rotate each figure the given distance. Sketch the new shape and label the points. Rotate the figure 180 Rotate the figure 90 Rotate the figure 270 Rotate the figure 180 Looks the same only the corners would move.
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