2. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Do Now: Aim: Let’s look at Reflections and ask ‘whuch u lookin’ at’?

3. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Line Symmetry A figure has LINE SYMMETRY if at least one line can be drawn through the figure so that half of it is mirrored. A T Lines of symmetry or reflection

4. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Rotational Symmetry Do either of these regular polygons have rotational symmetry? If so, how many degrees is required for each figure to coincide with the original? A figure has ROTATIONAL SYMMETRY if the figure coincides with itself when it is rotated 180 0 or less in either direction. Rotated 60 0, an regular hexagon will coincide with the original. 120 0 Rotated 120 0, an equilateral triangle will coincide with the original triangle 60 0

5. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Point Symmetry A figure has POINT SYMMETRY if the figure coincides with itself when it is rotated 180 0 in either direction. H H H H H H

6. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Point & Line Symmetries

7. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Reflection Properties: The Image is congruent to the Original The Orientation of Image is reversed (right is left and left is right) OriginalImage Line of Reflection The Line of Reflection is perpendicular to and bisects any segment connecting corresponding points on the Image and the Original figure.

8. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Reflections in Coordinate Geometry C’ is the mirror image of C D’ is the mirror image of D E’ is the mirror image of E m D C’ D’ C EE’ Line m acts like a mirror and is called the LINE OF REFLECTION or LINE OF SYMMETRY Reflections in Coordinate Geometry  CDE is reflected in the y-axis  C’D’E’ is mirror image of  CDE

9. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Reflections in Coordinate Geometry P(3, 2) What are the images of points P & S reflected through the y-axis? (r y ) y x S(1, 4) What are the images of points P & S reflected through the x-axis? P’(-3, 2) S’(-1, 4) S(1, 4)  S’(-1, 4) P”(3, -2) P(3, 2)  P”(3, -2) S”(1, -4) S(1, 4)  S”(1, -4) P(3, 2)  P’(-3, 2)

10. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Reflections in Coordinate Geometry P’(-x, y)P(x, y) Under reflection in the y-axis (r y ), the Image of P(x, y) is P’(-x, y) y x Under reflection in the x-axis, the Image of P(x, y)  P"(x, -y) P”(x, -y) P(x, y)  P’(-x, y) P(x, y)  P”(x, -y)

11. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Reflections through the Origin P’(-x, y) P(x, y) Under reflection in the origin (r o ), the Image of P(x, y) is ? y x Under reflection in the origin, the Image of P(x, y)  P”(-x, -y) P”(-x, -y) What is the image of (-3,4) under a reflection in the origin? (3,-4) (-3, 4) (3, -4)

12. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Reflections through the y = x P(x, y) Under reflection in y = x (r y = x ), the Image of P(x, y) is ? y x (3, 1) P’(y, x) (1, 3) y = x Under reflection in the y = x, the Image of P(x, y)  P’(y, x) What is the image of (-3,4) under a reflection in y = x? (4,-3)

13. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Model Problem Plot  ABC: A(-3, 1), B(-1, 5) and C(-2, -5). Plot  A’B’C’, the image of  ABC under a reflection in the y-axis (r y ) and write the coordinates. y A(-3, 1) B(-1, 5) C(-2, -5) A’(3, 1) B’(1, 5) C’(2, -5)

14. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Model Problem If the point (-4, -3) is reflected over the x-axis, what are the coordinates of the image? If the point (2, -1) is reflected over x = 1, what are the coordinates of the image? (2, -1) x = 1 (-4, -3) (0, -1) (-4, 3)

15. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Model Problem Plot  ABC: A(0, 4), B(-3, 6) and C(-4, 2). Plot  A’B’C’, the image of  ABC under a reflection in the origin (r O ) and write the coordinates. y A(0,4) B(-3,6) C(–4,2) A’(0,-4) B’(3, -6) C’(4, -2) Under reflection in the origin, the Image of P(x, y)  P”(-x, -y)

16. Aim: Transformation: Reflection Course: Alg. 2 & Trig. Model Problem