This document discusses different types of geometrical transformations including reflection, rotation, and dilation. It provides details on: 1) The 7 types of reflection - reflection across the x-axis, y-axis, lines y=x, y=-x, point (0,0), and lines x=k and y=k. 2) Rotation involving rotating objects around a fixed axis, including rotation around the origin (0,0) and a point (m,n). 3) Dilation, which enlarges or reduces the size of objects using a scale factor, applied to a point centered at either the origin or a point (k,l). 4) Examples of finding the image

1. GeometricalTransformation
(Reflection, Rotation, Dilatation)
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. Dilated
Dilation is also called the magnification or reduction of an object. If
transformations in translation, reflection, and rotation only change the
position of objects, then dilation transforms geometry by changing the size of
objects.The size of objects can be bigger or smaller.This change depends on
the scale that is the factor that is the factor.There are two formulas in dilation,
which are distinguished by the center. Next consider the description of the
formula for geometry transformation in the dilation below.

18. Dilate point A (a, b) to center O (0,0) with a
scale factor of m

19. Dilate point A (a, b) to center P (k, l) with a
scale factor of m