Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line...
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Transcript of Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line...
![Page 1: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/1.jpg)
Transformations
![Page 2: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/2.jpg)
Reflections
Lines of symmetry do not always have to touch the object
Mirror line
Object Image
![Page 3: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/3.jpg)
Object
Mirror line
Image
![Page 4: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/4.jpg)
Copy these axes on to squared paper
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -4 -3 -2 -1 0 1 2 3 4 5x
y
Plot these points
A(1, 2), B(2, 4) C(5, 1)
A
B
C Reflect triangle ABC in the x-axis to get a new triangle A1B1C1
A1
B1
C1
Reflect triangle ABC in the y-axis to get a new triangle A2B2C2
A2
B2
C2
Reflect triangle ABC in the y = -x to get a new triangle A3B3C3
A3
B3
C3
y x
Join the points to get triangle ABC
![Page 5: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/5.jpg)
Translations
A translation can be thought as a sliding movement
4 squares
Translate the triangle 4 squares to the right
![Page 6: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/6.jpg)
3 squares
Translate the triangle 3 squares upwards
![Page 7: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/7.jpg)
4 squares
Translate the triangle 4 squares to the right and 3 squares upwards
3 squares
This is written as
Translation4
3
Movement right or left
Movement up or down
![Page 8: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/8.jpg)
For translating the triangle 4 squares to the right and 3 squares upwards the movement can be thought as like this
Translation4
3
![Page 9: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/9.jpg)
For translating the triangle 3 squares to the left and 4 squares downwards the movement can be thought as like this
Translation3
4
This is written as
![Page 10: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/10.jpg)
RotationsIn a rotation an object is turned about a point through an angle. The point is called the centre of rotation.
Centre of rotation
A1B1
C1
A
B
C
Anticlockwise rotations are positive and clockwise are negative
Rotate triangle ABC about O through to get a new triangle A1B1C1
90
O
![Page 11: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/11.jpg)
A
B
C
Rotate triangle ABC about O through to get a new triangle A1B1C1
180
O
The centre of rotation can be in different places
Centre of rotationA1
B1
C1
![Page 12: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/12.jpg)
EnlargementAn enlargement changes the size of an object. The change is the same in all directions
Enlarge the rectangle by a scale factor of 2
3 squares
2 squares
6 squares
4 squares
![Page 13: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/13.jpg)
Enlargements are normally done from a centre of enlargement.
O
Measure the distance from the centre O to the vertex A on the triangle
Then multiply this distance by the scale factor. Label this point A1
Repeat for the other vertices B and C
Enlarge the triangle ABC by a scale factor 2. Use O as the centre of enlargement.
AB
C
A1B1
C1
![Page 14: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/14.jpg)
Enlarge the triangle ABC by a scale factor 3. Use O as the centre of enlargement.
The centre of enlargement does not always have to be in the same place
AB
C
O
A1B1
C1
![Page 15: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/15.jpg)
The scale factor can also be less than 1
O
Enlarge the triangle ABC by a scale factor . Use O as the centre of enlargement.
12
AB
C
A1B1
C1
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The scale factor can also be less than 0
O
Enlarge the triangle ABC by a scale factor -2. Use O as the centre of enlargement.
Notice that the image A1B1C1 is inverted
B
A
C
A1
B1 C1
![Page 17: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/17.jpg)
To find the mirror line of a reflection given the object and its image
A
B
C
A1
B1
C1
Join two corresponding points on the object and its image AA1
Construct the perpendicular bisector of this line segment
Perpendicular bisector of AA1 i.e. mirror line
![Page 18: Transformations. Reflections Lines of symmetry do not always have to touch the object Mirror line ObjectImage.](https://reader035.fdocuments.in/reader035/viewer/2022062423/5697bf8a1a28abf838c8a7e7/html5/thumbnails/18.jpg)
A1
B1
C1
A
BC
Centre of rotation
To find the centre of rotation given an object and its image
Join two corresponding points on the object and its image AA1
Draw the perpendicular bisector of this line segment
Repeat for two other corresponding points BB1