2.  Students will be able… › Identify reflections, rotations, and translations. › Graph transformations in the coordinate plane.

3. 1. Find the circumference and area of a circle with radius 5. 2. Find the distance between point J and point T. J(7, 1) and T(-2, -4)

10.  Transformation  A change in position, size, or shape of a figure. Does anyone know of a type of transformation?

11. TypePictureDefinition Reflection (flip)-A transformation across a line. -Each point and it’s image are the same distance from the line of reflection

12. 1. Fold your paper in half. Draw the line that is formed by the fold. 2. Label the fold “Line of Reflection” 3. Draw a triangle on one side of your paper. Label the vertices. 4. Place your Mira on the fold of your paper. 5. Look through the Mira to draw it’s reflection. Label the vertices as you see them in the Mira. * You have now constructed a Reflection. We will look at the characteristics that are present!

13.  Draw a line from A to A’. › Find the measure from A to the line of reflection. › Find the measure from A’ to the line of reflection. What do you notice? Equal Distance! You could continue this for B to B’ and C to C’

15. TypePictureDefinition Reflection (flip)-A transformation across a line. -Each point and it’s image are the same distance from the line of reflection Rotation (turn)- P is the center of rotation. - Each point and its image are the same distance from P. P

16. 1. Draw a rectangle or a triangle. (Go over it with a marker so you can really see it) 2. Label a point P outside of your figure. › This is your point of reflection 3. Take another sheet of paper and place it over the top of the figure. TRACE EVERYTHING (the figure and the point of reflection) 4. Place the copied figure underneath the original. Line up all points.

17. 5. Rotate the figure underneath the original. Make sure that point P is still lined up. 6. Redraw this figure labeling the new points with apostrophes. 7. Measure the distance from… C to P and C’ to P B to P and B’ to P A to P and A’ to P What do you notice?

18.  When you can identify a specific degree of turn for a rotation you should write it.  For example rotation 90°, 180°, 270°

19. TypePictureDefinition Reflection (flip)-A transformation across a line. -Each point and it’s image are the same distance from the line of reflection Rotation (turn)- P is the center of rotation. - Each point and its image are the same distance from P. Translation (Slide)- All points in the figure move the same distance in the same direction. P

20.  Preimage › The original figure.  Image › The figure after it is reflected, rotated or translated. › Has the apostrophes

21.  Preimage  Image A A’ B B’ C C’

22. 1. Write the type of transformation. 2. Label the preimage figure. 3. Write an arrow. 4. Label the image (label the same points in the same order just use an apostrophe ‘ ).

25. Identify each transformation. Then use arrow notation to describe the transformation.

29. 1. A figure has vertices at A(-1, 4), B(-1, 1), and C(3, 1). After a transformation, the image of the figure has vertices at A’(-1, -4), B’(-1, -1), and C’(3, -1). Draw the preimage and image. Then identify the transformation. Reflection across the x-axis.

30. 1. A figure has vertices at E(2, 0), F(2, -1), G(5, -1) and H(5, 0). After a transformation, the image of the figure has vertices at E’(0, 2), F’(1, 2), G’(1, 5) and H’(0, 5). Draw the preimage and image. Then identify the transformation. Rotation, 90°

31.  Without looking back at your notes who can tell me all three types of transformations?