Presentation about dilation, reflection, and translation

1. DILATATION
REFLECTION
TRANSLATION
By Sarah Walpole
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2. DILATATION
1st Topic
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3. • Dilation is also called the
magnification or reduction
of an object.
• But it does not change the
shape.
What is
dilatation?

4. • If the point is P(x,y) dialated with
the main point of O(0,0) and
with the scale factor of m the
shadow will be in the point of P’
(x’,y’).
• The relationship between the
points of P(x,y) and P’(x’,y’) can
be stated in the picture.
Dilates with the
center point O (0,0)

5. • The point of A(a, b) dilated to
the center point of P(k,l) with
the factor scale of m.
• Get a shadow with the point of
A’(a’, b’) and with the point of
a’- a = m (a - k) dan b’- b = m
(b - l).
Dialates with the
center point of P(k,l)

6. Dilation centered on point (3, 1) with a scale factor of 3, maps the point (5, b) to
point (a, 10). Then the value of a - b is
Problem solving of Dilation
Dilating with the center
(3, 1) with a scale factor
of 3 will produce the
following transformation
matrix
So that the value obtained
so the value is

7. TRANSLASIO
N
2nd Topic
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8. • Transformations: It is a change that occurs that maps or moves a shape in a
specific directions onto an image. These are translations, rotations, reflections,
and dilations.
• Pre-image: The position of the shape before the change is made.
• Image: The position of the shape after the change is made.
• Translation: A transformation that “slides” a shape to another location
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What is Translasion?

9. • You “slide” a shape up, down, right, left or all the above.
• Notation: (x, y) ( x + 2, y - 3)
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How translation work?

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Example

11. 11
Contoh rumus Translasi

12. • Determine the line shadow y = 3x – 5 by translation T (-2,1)!
Y’ – 1 = 3(x’+2) – 5
Y’ – 1 + 3x’ + 6 – 5
Y’= 3x’ + 2
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Problem Solving Translation

13. REFLEKSION
3rd Topic
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14. • The next discussion is reflection.
• 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 and 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.
What is Reflection?

15. Type of Reflection

16. Example of Reflection 16
against the x axis

17. Another Example 17
against the y axis

18. Probelemsolving 18
The line equation of 3x - y - 11 = 0 because of the
reflection on the line y = x, followed by the
transformation corresponding to the matrix
−3 2
−1 1
Try to find the equation that is shown.

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