A transformation is a change in the position, size, or

1. A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called a mapping. Examples of transformations are: translations, reflections, rotations, and dilations.

2. Preimage: the original figure Image: the figure after the transformation

3. Isometry: a transformation that does not change the size or shape of a figure Which of the transformations are examples of isometry? Translations, reflections, and rotations

4. Reflections 12-1 I CAN - Accurately reflect a figure in space. - Reflect a figure across the x-axis, the y-axis the line y = x, or the line y = –x Holt Geometry

5. Reflection: Reflection is a transformation that moves a figure by flipping it across a line

6. Reflection The original figure is called the preimageand the reflected figure is called the image. A reflection is the reflected image always congruent to the preimage? What do we call this?

7. Example 1: Identifying Reflections Tell whether each transformation appears to be a reflection. Explain. B. A. No; the image does not Appear to be flipped. Yes; the image appears to be flipped across a line.

8. Check It Out! Example 1 Tell whether each transformation appears to be a reflection. a. b. Yes; the image appears to be flipped across a line. No; the figure does not appear to be flipped.

9. We are going to reflect images on the coordinate plane across given lines 

11. Reflecting across vertical lines (x = a) Reflect across x = -2 Step 1 – Draw line of reflection B' A B A' Step 2 – Pick a starting point, count over-ALWAYS vertically or horizontally to line D C D' C' Step 3 –Go that same distance on the other side of line Step 4 – LABEL THE NEW POINTS Step 5 – Continue with other points Do # 3 on your worksheet Label the coordinates of the preimage.

12. Reflecting across y-axis Reflect the following shape across the y-axis Pre-image Image A'( , ) A( , ) A B( , ) B'( , ) B C( , ) C'( , ) C Do # 4 on your worksheet Label the coordinates of the preimage.

13. Reflecting across x-axis Reflect the following shape across the x-axis Pre-image Image A'( , ) A( , ) A B( , ) B'( , ) B C C( , ) C'( , ) Do #5 on your worksheet Label the coordinates of the preimage.

14. Reflecting across the line y = x Remember: Move ONLY verticallyor horizontally…think about why? Pre-Image Image F( , ) F'( , ) I( , ) I'( ,) F I S( , ) S'( , ) H( , ) H'( , ) Do #6 on your worksheet Label the coordinates of the preimage. H S

15. Look back at the problems you just completed. Compare the x and y-coordinates for the pre-image and image. Can you see a rule for each reflection?

17. S V U T S(3, 4) S’(3, –4) T’ U’ T(3, 1) T’(3, –1) U(–2, 1) U’(–2, –1) S’ V’ V(–2, 4) V’(–2, –4) Check It Out! Reflect the rectangle with vertices S(3, 4), T(3, 1), U(–2, 1) and V(–2, 4) across the x-axis. The reflection of (x, y) is (x,–y). Graph the image and preimage.

18. Reflect across y = –x C’( , ) A’( , ) K’( , ) E’( , ) A K C E Do #8 on your worksheet

19. Lesson Quiz Reflect the figure with the given vertices across the given line. 1.A(2, 3), B(–1, 5), C(4,–1); y = x A’(3, 2), B’(5,–1), C’(–1, 4) 2.U(–8, 2), V(–3, –1), W(3, 3); y-axis U’(8, 2), V’(3, –1), W’(–3, 3) 3.E(–3, –2), F(6, –4), G(–2, 1); x-axis E’(–3, 2), F’(6, 4), G’(–2, –1)