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Reflection Transformations and its lines of Symmetries

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- 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
- 6. DILATION- Changes the size of the object
- 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)
- 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