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9. GEOMETRICAL
TRANSFORMATION
DR. FARHANA SHAHEEN
REFLECTIONS
Types of Transformations
• 1. Translation (Slide)
• 2. Reflection (Flip)
• 3. Rotation (Turn)
• 4. Dilation (Change in size)
Examples: Types of Transformations
Notations:
•Pre-Image
•Image
DILATION- Changes the size of the object
CONGRUENCE TRANSFORMATIONS
Isometric
Transformations
Note: Dilation is Not Isometric.
https://www.youtube.com/watch?v=BkaI_3Y-chc
Isometric
Transformations
• Translation (Slide)
• Reflection (Flip)
• Rotation (Turn)
Types of
Transformations
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
Reflection along x- and y-axis
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.
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.
Animation Challenge Roundup:
Transformations!
• https://www.youtube.com/watch?v=21aWtuJanx8

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Geometrical transformation reflections