R90 (x,y)  Rotate the point (x, y) 90 counterclockwise - ppt

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Rotations Rotate the shape T anticlockwise center T T T T y x x y T Rotate the shape T anticlockwise center T T T
R90 (x,y)  Rotate the point (x, y) 90 counterclockwise
ROTATIONS. A rotation is a transformation that TURNS a figure around the origin (0, 0). A rotation can move in two directions, clockwise or counterclockwise. A COUNTERCLOCKWISE rotation is a POSITIVE rotation. A CLOCKWISE rotation is a NEGATIVE rotation. R90 (x,y)  Rotate the point (x, y) 90 counterclockwise. R-90 (x,y)  Rotate the point (x, y) 90 clockwise. Notice the angle between the pre-image, the origin & the image is equal to the degree of rotation!
x. y. T. Rotate the shape T. anticlockwise. center. T. T. T.
It doesn’t say anticlockwise or counterclockwise so you have to understand that a positive turn is a counterclockwise turn.
x. y. T. Rotate the shape T. anticlockwise. center. T. T. T T. T. T.
x. y. T. T. T. Rotate the shape T. clockwise. center. T.
Direction of rotation. In order to find the image, using this information it is. best to use tracing paper.
Direction of rotation. clockwise. Put a piece of tracing paper. over the drawing. Copy the object onto the. tracing paper. A. A’ Put a pencil on the tracing. paper – point at the centre. of rotation. X. Rotate the tracing paper. by the required amount in. the specified direction. Note the end point of the object. Remove the tracing paper and. draw the image and label it.
Rotate shape A : 90o c/w about the origin and. label it ‘a. b) 180o c/w about the origin and. label it ‘b’ c) 90o anti c/w about the origin and. label it ‘c’ d) 90o c/w about the (2,2) and. label it ‘d’ e) 90o anti c/w about the (-2,1) and. label it ‘e’ f) 90o anti c/w about the (-4,6) and. label it ‘f’ g) 90o anti c/w about the (1,8) and. label it ‘g’ A
90o c/w about the origin. and label it ‘a’ b) 180o c/w about the origin. and label it ‘b’ 90o counter c/w about the. Origin and label it ‘c’ d) 90o c/w about the (2,2) and label it ‘d’ e) 90o counter c/w about the (-2,1) and label it ‘e’ f) 90o counter c/w about the (-4,6) and label it ‘f’ g) 90o counter c/w about the (1,8) and label it ‘g’ y-axis x-axis x. f. d. x. A. g. a. x. x. e. x. c. b.
x. y. T. Rotate the shape T. anticlockwise. centre. T. T. T. What are the new coordinates of the triangle How can you work them out without drawing a grid or the shape
anticlockwise center. Explain how to get from the left hand coordinate to the right hand coordinate. Change the sign of the y coordinate and then swap the coordinates around.
x. y. T. Rotate the shape T. anticlockwise. center. T. T. T T. T. T. What are the new coordinates of the triangle How can you work them out without drawing a grid or the shape
anticlockwise center. Explain how to get from the left hand coordinate to the right hand coordinate. Change the sign of the x coordinate and change the sign of the y coordinate.
x. y. T. T. T. Rotate the shape T. clockwise. center. T. What are the new coordinates of the triangle How can you work them out without drawing a grid or the shape
clockwise center. Explain how to get from the left hand coordinate to the right hand coordinate. Just change the sign of the x coordinate and then swap the coordinates around.
Rules for POSITIVE, COUNTER CLOCKWISE Rotations. Given ABC with A(1, 1), B(4, 1), and C(1, 3) (-1,1) (-1,4) (-3, 1) B’ R90 (x,y)  (-y, x) Switch and negate the 1st. R180(x, y)  (-x,-y) Negate both. R270(x, y)  (y, -x) Switch & Negate the 2nd. C. C. A’ C’ A. B. (-1, -1) (-4, -1) (-1, -3) B A A ’ C ’ (1, -1) (3, -1) (1, -4) C B ’
90 degrees counterclockwise around origin: (x, y) (-y, x) 180 degrees around the origin: (x, y)  (-x, -y) 270 degrees counterclockwise around origin: (x, y)  (y, -x)
to the corresponding point. on the image. B. C. A. Object. Draw the perpendicular. bisector for the connecting. lines. 75o. x. The centre of rotation is. where the perpendicular. bisectors cross. C’ B’ A’ 75o anticlockwise. Image. The alternative (easier) method. is to trace the object onto tracing. paper and use trial and error.
Find the centre of rotation for. each of these rotations. A onto B. A onto C. A onto D. D onto B. B onto F. A onto E. C onto G. H onto A. B onto E. D onto C. y-axis x-axis A. B. F. G. H. C. D. 90o c/w centre (0,0) E. 180o c/w or ac/w centre (0,0) 270o c/w or 90o ac/w centre (0,0) 270o c/w or 90o ac/w centre (0,0) 90o c/w centre (2,-2) 90o ac/w centre (2,6) 90o c/w centre (-2,-1) 180o c/w or ac/w centre (0,4) 180o c/w or ac/w centre (4,2) 90o ac/w centre (0,0)
and label it ‘a’ b) 180o c/w about the origin. and label it ‘b’ c) 90o anti c/w about the origin. and label it ‘c’ d) 90o c/w about the (2,2) and label it ‘d’ e) 90o anti c/w about the (-2,1) and label it ‘e’ f) 90o anti c/w about the (-4,6) and label it ‘f’ g) 90o anti c/w about the (1,8) and label it ‘g’ Find the centre of rotation for. each of these rotations. A onto B. b) A onto C. c) A onto D. d) D onto B. e) B onto F. f) A onto E. C onto G. H onto A. B onto E. D onto C. A A. B. F. G. H. C. D.
Identify reflection symmetry in 3-D solids. C Grade Rotate shapes about any point. Describe rotations fully about any point. Find the centre of rotation and describe it fully.
Rotation. Centre of rotation. Angle of rotation. 30o. Direction of rotation. clockwise. If you are asked to rotate and object. by an angle that you have to measure. follow the same steps and: 30o. A’ A. Mark a line from the centre of rotation. to use as 0o and also mark this on the. same place on the tracing paper. X. Before putting the tracing paper on. measure the required angle, and draw. a line accordingly.