This document discusses different types of geometrical transformations including reflection, rotation, and translation. It describes 7 types of reflections based on axes or lines of reflection. Rotation is defined as spinning an object around a fixed axis, and it provides examples of rotations centered around different points. Translation is defined as shifting an object to a new position by adding a certain distance to the x- and y-coordinates. The document also includes examples of applying these transformations to points.

1. GeometricalTransformation
(Reflection, Rotation,Translation)
By: Nicholas Charles XI-BS-1

2. Reflection
Mirroring is more commonly known as reflection. Like the shadow of an object
formed from a mirror. An object that experiences reflection will have a shadow
of an object produced by a mirror.The result of reflection in the cartesian
plane depends on the axis that is the mirror.There are seven types of
reflection material that will be provided.These types include reflection on the
x axis, y axis, line y = x, line y = -x, point O (0,0), line x = h, and line y = k.The
following is a summary of the list of transformation matrices for reflection /
reflection.

3. Reflection towards x axis

4. Reflection towards y axis

5. Reflection towards line x

6. Reflections towards line y

7. Reflection towards the origin

8. Reflection towards line x=k

9. Reflection towards line y=k

10. Question
Tentukan bayangan titik a (2,3) yang dicerminkan tehadap garis y = -x!
Penyelesaikan:
A(2,3) berarti x = 2 dan y=3
X’ = -y = -3
Y’ = -x = -2
Jadi, bayangan titik a(2,3) adalah A’(-3,-2)

11. Rotation
Rotation is the rotation of objects on a fixed axis, for example spinning and
rotation of the earth on the axis / axis. For the earth, this rotation occurs on the
north-south axis / axis.

12. Rotation with center O (0,0) as big as alpha

13. Rotation with Center (M,n) as big as alpha

14. Rotation with Center o (0,0) as big as alpha
then as big as beta

15. Rotation with center (m,n) as big as alpha then
as big as beta

16. Question
Titik a dirotasikan terhadap titik O (0,0) sejauh 90 derajat berlawanan dengan arah putaran jam.Tentukan titik
bayangan A.
Pembahasan:
(x’y’)=(01-10).(xy)
(x’y’)=(01-10).(21)
(x’y’)=(-12)
Dengan demikian x’ = -1 dan y’ = 2.
Jadi, bayangan titik A(2,1) oleh rotasi terhadap titik O (0,0) sejauh 90 derajat berlawanan arah putaran jam
adalah A’ (-1,2).

17. Translation
Translation is a change in an object by shifting objects from one position to
another with a certain distance. Determining the results of objects through
translation is quite easy.The method is only by adding abscissa and ordinate
with a certain distance in accordance with the provisions. For more details
about the translation process can be seen in the picture below.

18. Example ofTranslation