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### High School Mathematics13.7 Trasformations Review - Reflection, Rotation, Translation and Dilation

 1. The process of getting the point P1, from any point P by making use of a line 'l' is called reflection in the l or symmetric mapping with respect to l. 2. If l(P) = P1, then l(p1) = P Then l is the perpendicular bisector of PP1. 3. Reflection maps the plane onto itself it preserves distance, angle measures collinearity, betweenness and areas. 4. Reflection reverses the orientation of the plane. 5. Points on the axis of reflection are invariant or fixed points and the line is a fixed line. 6. A line perpendicular to l is mapping onto itself when reflected in l. 7. Two figures are said to be congruent if one can be obtained from the other by one more reflections. 8. Reflection of (x,y) in X-axis is (x,-y). 9. Reflection of (x,y) in Y-axis is (-x,y), 10. Even number of reflections retains the orientation of the plane, odd number of reflections reverses the orientation of the plane. 11. If l ^ m, then lm = ml. If l and m are intersecting lines then lm ¹ ml. 12. A mapping of a plane in which each point of the plane moves in the same direction through the same distance is called translation. 13. Two successive reflections in a pair of parallel lines is a translation. Two successive reflections in a pair of intersecting lines in a rotation. 14. Translation preserves lengths, angle measures, parallelism, perpendicularity, collinearity, betweenness and orientation. 15. There are no fixed points in translation. 16. The line along which translation is made and the lines parallel to it are fixed lines. 17. Rotation preserves lengths, angle measures and orientation. 18. In rotation, the centre of rotation is the only fixed point. 19. (a) Oa + b = Ob + a. (b) O+900(x,y) ® (-y, x) (c) O-900(x,y) ® (y, -x) (d) O-1800(x,y) ® (-x, -y) 20. If a figure remains unaltered by reflection in a point O, the figure is said to be symmetric with respect to O. 21. A parallelogram has point symmetry. The intersection of the diagonals is the centre of symmetry. Directions: Choose the correct answer.
 Q 1: Rotation preserves the shape and size of the figures.TrueFalse Q 2: Rotation has only one fixed point that is the centre of rotation.TrueFalse Q 3: Image of (2,5) under translation defined by (x,y) ® (x+3, y+3).(8,5)(5,8) Q 4: Image of (1,4) under translation defined by (x,y) ® (x+1, y-1).(3,2)(2,3) Q 5: Rotation preserves the position of the figures.TrueFalse Q 6: In translation, the distance between any two points of a figure and their corresponding images remains the same.TrueFalse Q 7: In translation, the shape of a figure is changed.FalseTrue Q 8: In, translation, the orientation of the plane is not alterned.FalseTrue Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!