1. GEOMETRY
ANGLE AND PLANE

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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.
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3. 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
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4. 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
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5. 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
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6. 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, – 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
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7. 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
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8. 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 (- ½ )
= - ½ =
y’ = x sin y cos
= -1 Sin(-450) + 4 Cos(-450)
= -1(-½ ) ½
= ½
= 5/2 (
Then Q’ (3/ , 5/ )
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9. 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 ‘
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10. 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, ) = P’ (4, 12)r
P(2, 6) P’ ( ½ . 2, ½ . 6) = P’ (1, 3)
(0, 2)
(0, ½ )
Then P’(1, 3)
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THANK YOU
GOOD LUCK
Keep studying
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