8.Transformations
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21 8. Transformations 3.2 Reflections Write : Reflection on axis Example: Draw image under reflection on PQ 2. The polygon A’B’C’D’E’ is the image polygon ABCDE under the certain transformation W. Describe in full the transformation W. …………………………………………… …………………………………………… …………………………………………… Example: 1. Draw the image of triangle ABC under the reflection on axis (a) x=1 (b) y=1 (c) x (d) y (e) AB C A B 2. Diagram A’B’C’D’E’F’ABCDEF is the image of diagram ABCDEF under the certain transformation P. Describe the transformation P. A A’ B B’ D C C’ D’ F E E’ F’ …………………………………………… …………………………………………… Exercise 11: 1. Figure P is the image of figure Q under the certain transformation W. P A Q -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 4 C 3 2 1 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 4 C 3 2 1 - 3 -2 -1 0 1 2 3 4 5 -1 -2 -3 4 C 3 2 1 Q P P Q
Transcript of 8.Transformations
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8. Transformations 3.2 Reflections Write : Reflection on axis Example: Draw image under reflection on PQ 2. The polygon A’B’C’D’E’ is the image polygon ABCDE under the certain transformation W. Describe in full the transformation W. …………………………………………… …………………………………………… …………………………………………… Example: 1. Draw the image of triangle ABC under the reflection on axis (a) x = 1 (b) y = 1 (c) x (d) y (e) AB
C A B 2. Diagram A’B’C’D’E’F’ABCDEF is the image of diagram ABCDEF under the certain transformation P. Describe the transformation P. A A’ B B’ D C C’ D’ F E E’ F’ …………………………………………… …………………………………………… Exercise 11: 1. Figure P is the image of figure Q under the certain transformation W. P A Q
-3 -2 -1 0 1 2 3 4 5 -1
-2
-3
4 C
3
2
1
-3 -2 -1 0 1 2 3 4 5 -1
-2
-3
4 C
3
2
1
- 3 -2 -1 0 1 2 3 4 5 -1
-2
-3
4 C
3
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1
Q
P
P
Q
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(a) Describe the transformation W …………………………………………………………… …………………………………………………………… (b) Mark and name the coordinate of the
image coordinate A under the same transformation.
…………………………………………………………… …………………………………………………………… 13. PMR 2005 Diagram below shows two quadrilateral, ABCD and A’B’C’D’, draw on a grid of equal squares. A’B’C’D’ is the image of ABCD under a reflection. On the diagram, draw the axis of reflection. [2 marks]
14. PMR 2006 Diagram below shows object P and straight line MN drawn on a grid of equal squares. On the diagram in the answer space, draw the image of P under a reflection in the straight line MN.
[2 marks]
8.2 Translations
Write ; Translation ⎟⎟⎠
⎞⎜⎜⎝
⎛yx
Where: x is moved parallel with x – axis [If moved to right side, the sign is (+) and Moved to left side, the sign is (-) ] y is moved parallel with y-axis [If moved to up ward, the sign is (+) and Moved to down ward, the sign is (-) ]
Example: 1. Draw and label the image of triangle P
under the translations ⎟⎟⎠
⎞⎜⎜⎝
⎛−12
2. The diagram Q is the image diagram P under the certain transformation W. Describe in full the transformation W. …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… ……………………………………………………………
P
P
Q
A
B
D C
D’
C’ B’
A’
P
M
N
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Example 2: 1. Draw the image of triangle ABC under the reflection C A B 2. Diagram A’B’C’D’E’F’ABCDEF is the image of diagram ABCDEF under the certain transformation P. Describe the transformation P. A B E F A’ B’ C D E’ F’ C’ D’ …………………………………………… …………………………………………… …………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… ……………………………………………………………
Exercise 11: 1. Figure P is the image of figure Q under the certain transformation W. P A Q (a) Describe the transformation W …………………………………………… …………………………………………… (b) Mark and name the coordinate of the image
coordinate A under the same transformation.
…………………………………………… …………………………………………… 2. PMR 2004 In diagram below P’ is the image of P under transformation M
Describe in full transformation M. [2 marks]
…………………………………………… ……………………………………………
-3 -2 -1 0 1 2 3 4 5 -1
-2
-3
4 C
3
2
1
-3 -2 -1 0 1 2 3 4 5 -1
-2
-3
4 C
3
2
1
-3 -2 -1 0 1 2 3 4 5 -1
-2
-3
4 C
3
2
1
2
02 4
4
6
6
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8
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10
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12
P’
P
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3. PMR 2006 Diagram below shows two polygon, H and H’, drawn on a grid of equal squares with sides of 1 unit. H’ is the image of H under transformation L. Describe in full transformation L. [2 marks]
…………………………………………………..
………………………………………………….. 8.3 Rotation Write : Rotation about centre (x,y) @ A thought 90 clockwise @ anti clockwise. Example: 1. Draw the image of P under the rotation about centre O, 90 clockwise (a) (b)
(c) 2 The diagram P is the image diagram Q under the certain transformation W. Describe the transformation W. To Find the centre of rotation
1. Join the corresponding vertex 2. Draw the perpendicular bisector 3. Intersect of two perpendicular line is a
center of rotation. …………………………………………… …………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… ……………………………………………………………
P
O .
P O .
P O .
P
Q
H’
H
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Example: 1. Draw the image of triangle ABC under the rotation about point (1,1) through 900 anticlockwise. C A B 2. Diagram A’B’C’D’E’F’ABCDEF is the image of diagram ABCDEF under the certain transformation P. Describe the transformation P. A B D C F E …………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… ……………………………………………………………
17. PMR 2005 Diagram below shows three triangles, P,Q and R, which are drawn on a Cartesian plane.
(a) Q is the image of P under a rotation of
900. State (i) the direction of the rotation. (ii) the coordinates of the centre of the rotation.
(b) R is the image of P under transformation M. Describe in full transformation M.
[4 marks] …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… …………………………………………………………… ……………………………………………………………
-3 -2 -1 0 1 2 3 4 5 -1
-2
-3
4 C
3
2
1
-3 -2 -1 0 1 2 3 4 5 -1
-2
-3 -4
4 C
3
2
1
2
4
10
8
6
O 8 6 4 2 -4 -2
P
R
Q
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8.4 Enlargement Write : Enlargement at centre (x, y) @ P with scale factor k Example: 1. Draw the image of triangle ABC under an enlargement at centre (4,3) with scale factor 2 (a) (b) 2. Draw the image of triangle ABC under an
enlargement at centre (5,2) with scale factor 21
3. Draw the image of triangle ABC under an enlargement at centre (4,4) with scale factor - 2 4. The diagram P is the image diagram Q under the certain transformation W. Describe the transformation W. 1. Join corresponding point object and image. 2. Intersection point is the centre of enlargement ………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… …………………………………………… ……………………………………………
object theof side ingcorrespond oflength image theof side oflength k factor, scale =
P
P
P
P
P
Q
object theof side ingcorrespond oflength image theof side oflength k factor, scale =
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Exercise 12: 1. Figure P is the image of figure Q under the certain transformation W. P A Q (a) Describe the transformation W …………………………………………… …………………………………………… (b) Mark and name the coordinate of the image
coordinate A under the same transformation.
…………………………………………… …………………………………………… 5.5 Congruent Example: 1. PMR 2004 Diagram below in the answer space shows polygon ABCDEF and straight line PQ drawn on a grid of equal squares. Starting from the line PQ, draw polygon PQRSTU which is congruent to polygon ABCDEF.
NOTE
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-3 -2 -1 0 1 2 3 4 5 -1
-2
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4 C
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