This document discusses different types of geometrical transformations including translations, reflections, rotations, and dilations. It provides examples and notations for transformations and notes that dilation is not an isometric transformation. Reflections are further categorized by the line they are reflected across such as the x-axis, y-axis, lines of the form y=x, y=-x, y=k, x=k, and y=mx+c. Two examples of finding the line of reflection are given when points are mapped before and after a reflection.

1. 9. GEOMETRICAL
TRANSFORMATION
DR. FARHANA SHAHEEN

2. REFLECTIONS

3. Types of Transformations
• 1. Translation (Slide)
• 2. Reflection (Flip)
• 3. Rotation (Turn)
• 4. Dilation (Change in size)

4. Examples: Types of Transformations

5. Notations:
•Pre-Image
•Image

6. DILATION- Changes the size of the object

7. CONGRUENCE TRANSFORMATIONS

8. Isometric
Transformations
Note: Dilation is Not Isometric.
https://www.youtube.com/watch?v=BkaI_3Y-chc

9. Isometric
Transformations
• Translation (Slide)
• Reflection (Flip)
• Rotation (Turn)

10. Types of
Transformations

12. Types of
Reflection (Flip)
• 1. Reflection by x-axis
• 2. Reflection by y-axis
• 3. Reflection by line y=x
• 4. Reflection by line y=-x
• 5. Reflection by line y=k
• 6. Reflection by line x=k
• 7. Reflection by line y=mx+c

13. Reflection along x- and y-axis

19. Question: 1.
Find the equation of the line of reflection
• 1. Under a reflection, the point P(3,5) is mapped onto the point P’(5,3).
• (i) Find the equation of the line of reflection.
• Sol: If (x, y) ↔ (𝒚, 𝒙), then the equation of line of reflection is y = x.
• (ii) The point P’(5,3) is then reflected and the coordinates of the final
image is P”(-5, 3). Find the equation of the line of the second
reflection.
• Sol: If (x, y) ↔ (−𝒙, 𝒚), then the line of reflection is y-axis, or x = 0.

20. Question: 2.
To find the equation of line of reflection
• The points A and its image A’ is given below. Plot the points, construct
and find the equation of line of reflection in each case.
• (i) A (1, 1), A’(3,1) (ii) A (2, 1), A’(0,3) (iii) A (-1,1), A’(3,-1)
• Hint: Draw the perpendicular bisectors of the line AA’ by drawing arcs
up and down at points A and A’, and joining the points of intersection
of the arcs. This perpendicular bisector will be the line of reflection.
Take any two points on this line, (one can be the midpoint of AA’, and
other can be x- or y-intercepts, or both.

21. Animation Challenge Roundup:
Transformations!
• https://www.youtube.com/watch?v=21aWtuJanx8