GEOMETRY ANGLE AND PLANE

Isi dengan Judul Halaman Terkait Angle and Plane Standard Competence Determining line position and angle size that involves point, line and plane in two dimensions Base Competence: 3. Applying flat shape tranformation. Hal.: 2 Isi dengan Judul Halaman Terkait

Geometry Transformation 1. Translation Transformation translation of a point P(x,y) is by moving as far as a unit at axis x and b unit at axis y that notated by T = then become a point P’(x’, y’) and: x’ = x + a y’ = y + b See picture 1 P(x’,y’) P(x,y) x y Picture 1 HAL 6 Hal.: 3 Isi dengan Judul Halaman Terkait

Geometry Transformation Example of translation: Given that translation T = and point Q ( 1, 1), then Find the point coordinate Q’. 4 3 Answer: Q(1, 1) Q’=(1 + 4, 1 + 3) Q’=( 5, 4) See picture 2 P’(5,4) P(1,1) Picture 2 HAL 8 Hal.: 4 Isi dengan Judul Halaman Terkait

Geometry Transformation Isi dengan Judul Halaman Terkait 2. Reflection 2.1 Pencerminan terhadap garis x = a 2.1 Reflection towards line x = a A point P(x, y) reflected towards line x = a, can be written: M . x = a P (x, y) P’(2a – x, y) 2.2 Reflection towards line y = b A point P(x, y) reflected towards line y= b, can be written: P (x, y) P’(2a – x, y) M . y = b HAL 9 Hal.: 5 Isi dengan Judul Halaman Terkait

Geometry Transformation Example of Reflection: Determine point shadow P (2, 1) if reflected towards: a. Line x = 3 b. Line y = 5 Answer: a. P(2, 1) P’ (2 . 3 – 2, 1) = P’( 4, 1) b. P(2, 1) P’(2, 2 . 5 – 1) = P’(2, 9). M . x = 3 M . y = 5 See picture 3 P’(2, 9) . Picture 3 Y x = 3 y = 5 P(2,1) . .P’(4,1) X Hal.: 6 Isi dengan Judul Halaman Terkait

Geometry Transformation 3. Rotation Rotation is a transformation that moves every points on the flat shape by rotating very points and it is determined by: Angle size of rotation Center point of rotation Angle direction of rotation. See picture 4 At the rotation towards center point O(0,0) as big as radian with the positive direction then point P(x,y) become P’(x’,y’) that can be stated as: Y P’(x’,y’) P(x,y) x’ = x cos - y sin y’ = x sin + y cos X Hal.: 7 Isi dengan Judul Halaman Terkait

Geometry Transformation Next Rotation Point Q(-1, 4) rotated like hand of clock towards center point O, Determine the shadow point of Q by rotation (O, 450) Answer: = - 450 x’ = x cos - y sin = -1 Cos (- 450) – 4 sin (- 450) = - ½ - 4 . (- ½ ) = - ½ + 2 = y’ = x sin + y cos = -1 Sin(-450) + 4 Cos(-450) = -1(-½ ) + 4 . ½ = ½ + 2 = 5/2 ( Then Q’ (3/2 , 5/2 ) Hal.: 8 Isi dengan Judul Halaman Terkait

Geometry Transformation 4. Dilatasi (Multiplication) Dilatasi is a transformation that changes size (make it bigger or smaller) of a flat shape, but it will not change the model of shape: Dilatasi center Dilatasi factor or scale factor See the picture 5 C’ If P(x,y) multiplicated towards center O(0,0) and scale factor k gotten shadow P’(x’,y’) C B’ B O A x’ = k . x, y’ = k . y A ‘ Hal.: 9 Isi dengan Judul Halaman Terkait

Geometry Transformation Example of Dilatasi Determine the point shadow P(2,8) by dilatasi: (0, 2) (0, ½ ) Think it Solving problem: P(2, 8) P’ ( 2 . 2, 2 . 6 ) = P’ (4, 12)r P(2, 6) P’ ( ½ . 2, ½ . 6) = P’ (1, 3) (0, 2) (0, ½ ) Then P’(1, 3) Hal.: 10 Isi dengan Judul Halaman Terkait

Isi dengan Judul Halaman Terkait THANK YOU GOOD LUCK Keep studying Hal.: 11 Isi dengan Judul Halaman Terkait