MATEMATIKA SMP PROGRESSIVE BUMI SHALAWAT KOKOH SPIRITUAL, MAPAN INTELEKTUAL SOLEH CHUDIN, S.Pd. 1. Identify whether a figure has been reflected, rotated, or translated and delatation, 2. Label corresponding points on the image of a polygon following a transformation, 3. Perform a simple transformation on a grid given a coordinate transformation. HADIST OF THE DA COORDINATE SYSTEM Prerequisite material TRANSFORMATION TRANSLATION (PERGESERAN) REFLECTION (PENCERMINAN) ROTATION (PERPUTARAN) DELATATION (PERUBAHAN UKURAN) . From the figure we can see that the rotation of Suppose the toy plane moves around -90°, where are the coordinates of the plane's point P(30,10) is 90° counterclockwise towards destination in its Cartesian coordinates? point Q(–10,30). If we continue to rotate 90° A toy plane at coordinates P(30,10) From the 90 figure, that the rotation of from point Qdegrees wewe getcan thesee destination R(-30,–10) rotates counterclockwise point P(30,10) is -90° so it will be towards point Q. arriving at at point CanAfter we write: We cantowrite point Q, theS(10,-30). plane continues rotate π [π 30,10 ,90° 90 degrees from the origin to R. π 30,10 π point −10,30 π [π 30,10 ,−90° Show coordinates of the plane's π the 30,10 π [π −10,30 ,90° π 10, −30 destination in Cartesian coordinates! π −10,30 π −30, −10 y Q30 . 20 10 -40 . -30 -20 R 0 -10 10 -10 -20 -30 . S 20 30 P 40 x Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Rotating a shape means changing its orientation. • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Solution Ex1 Patterns are shown in pairs, below. Some patterns are rotations of each other and some are not. Circle the letter of the patterns which are not rotations of each other. [a] [d] [g] [b] [e] [h] [c] [f] [i] • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Solution Ex2 Rotate the shapes clockwise by the number of degrees given. ¼ turn 90o ½ turn 180o 270o ¾ turn [a] [b] [c] ` ` ` ` • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Solution Solution Q1 Circle the letter of the patterns which Q2 Rotate the shapes clockwise by the number of degrees given. are not rotations of each other. 90o 180o [a] [a] [b] [b] [c] [c] ` ` • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. ` KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Rotate to the right. Lightly place the pencil on the point and rotate. Half of a full-turn. Ex4 Rotate the following shape 180o anticlockwise about the given point. Solution Solution Ex3 Rotate the following shape 180o clockwise about the given point. Rotate to the left. Does direction matter o? when rotating by 180 Tracing paper Half of a full-turn. Tracing paper Lightly place the pencil on the point and rotate. • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform ¼ of a full-turn. Rotate to the right. Lightly place the pencil on the point and rotate. Ex6 Rotate the following shape 270o anticlockwise about the given point. Solution Solution Ex5 Rotate the following shape 90o clockwise about the given point. Rotate to the left. ¾ of a full-turn. Lightly place the pencil on the point and rotate. Tracing paper • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. Tracing paper KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Q2 Rotate the following shape 180o about the given point. Solution Solution Q1 Rotate the following shapes 180o about the given point. Tracing paper Tracing paper • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Q4 Rotate the following shape 180o about the given point. Solution Solution Q3 Rotate the following shapes 180o about the given point. Tracing paper • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. Tracing paper KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Q6 Rotate the following shape 90o anticlockwise about the given point. Solution Solution Q5 Rotate the following shape 270o clockwise about the given point. Tracing paper • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. Tracing paper KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Q8 Rotate the following shape 270o anticlockwise about the given point. Solution Solution Q7 Rotate the following shapes 90o clockwise about the given point. Tracing paper Tracing paper • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. Tracing paper Tracing paper KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform π¦ 11 10 9 8 7 6 5 4 3 2 1 Tracing paper Ex8 Rotate the following shape 180o about the point (-1, 1). Solution Solution Ex7 Rotate the following shape 270o anticlockwise about the point (4,5). π¦ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 Tracing paper -2 -3 -4 -5 1 2 3 4 5 π₯ 1 2 3 4 5 6 7 8 9 10 11 π₯ • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Q2 Solution Solution Q1 Rotate the following shape 90o clockwise about the point (1,2). π¦ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 Rotate the following shape 270o anticlockwise about the origin. Tracing paper Tracing paper 1 2 3 4 5 π₯ π¦ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. (0,0) 1 2 3 4 5 π₯ KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Q4 Solution Solution Q3 Rotate the following shape 180o clockwise about the point (-1,-2). π¦ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 Rotate the following shape 270o clockwise about the origin. π¦ Tracing paper 1 2 3 4 5 Tracing paper π₯ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. 1 2 3 4 5 π₯ KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform π¦ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 Q6 Solution Solution Q5 Rotate the following shape 270o anticlockwise about the point (0,2). Rotate the following shape 270o clockwise about the origin. Tracing paper Tracing paper 1 2 3 4 5 π₯ π¦ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. 1 2 3 4 5 π₯ KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform Solution Q7 Chris rotated each of the following shapes about the origin. He has rotated exactly two incorrectly. Shade the shapes in the wrong final position. 8 π¦ 6 4 2 -16 -14 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 14 16 π₯ -2 -4 -6 -8 • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS Wednesday, 16 August 2023 We are learning about: Rotation We are Key terms: learning Angle, to:(anti)clockwise, Perform and describe centre, image, rotations rotate, of shapes. transform . From the figure we plane can see that around the rotation Suppose the toy moves -90°,of are isthe coordinates of the plane'spoint pointwhere P(30,10) 90° anticlockwise towards destination in its Cartesian coordinates? Q(–10,30). If we continue to rotate 90° from From wethecan see P(30,10) that the rotation of A point toythe plane coordinates Qfigure, weatget destination R(-30,–10) point P(30,10) is -90° so it will be at point rotates 90 degrees anticlockwise Can we S(10,-30). Wewrite: can write towards point Q. After arriving at 30,10 ,90° to rotate point Q, the planeπ [πcontinues π 30,10 π [π 30,10 ,−90° π −10,30 90 degrees from the origin to point π 30,10 π 10,R.−30 π [π −10,30 ,90° plane's Showπthe coordinates of the −10,30 π −30, −10 destination in Cartesian coordinates! y Q30 . 20 10 -40 . -30 -20 R 0 -10 10 20 30 P 40 x -10 -20 -30 . S • Developing learners will be able to identify a rotated pattern. • Secure learners will be able to rotate patterns and shapes by 90o, 180o and 270o. • Excelling learners will be able to perform and describe a rotation around a given point at 90o, 180o and 270o. KEY TERMS What do you feel for this lesson today?? COORDINATE SYSTEM Prerequisite material TRANSFORMATION TRANSLATION (PERGESERAN) REFLECTION (PENCERMINAN) ROTATION (PERPUTARAN) DELATATION (PERUBAHAN UKURAN) QUOTE OF THE DAY THANK YOU
