Introduction and Review Information

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. A transformation is an isometry if the size and shape of the figure stay the same. Which of the transformations above are an isometry? Translations, reflections, and rotations

Every transformation has a pre-image and an image. Pre-image is the original figure in the transformation (the “before”). Its points are labeled as usual. Image is the shape that results from the transformation (the “after”). The points are labeled with the same letters but with a ' (prime) symbol after each letter.

Example Pre-Image Image A' A B B' C' C

Mapping A way of showing where you started and finished a transformation. It uses an arrow (→)

Remember equations for horizontal lines: Writing Equations Remember equations for horizontal lines: y = 2 is horizontal line crossing y-axis at 2 y = –4 is horizontal line crossing y-axis at 4 y=2 y =–4

Remember equations for vertical lines: Writing Equations Remember equations for vertical lines: x = 2 is vertical line crossing x-axis at 2 x = –4 is vertical line crossing x-axis at –4 x=2 x =–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

Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line.

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

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

Reflecting across vertical lines (x = a) Refer to “Reflections” Worksheet Example #3 Reflect across x = 2 Step 1 – Draw line of reflection A B B' A' Step 2 – Pick a starting point, count over-ALWAYS vertically or horizontally to line D C C' D' Step 3 – Go that same distance on the other side of line Step 4 – LABEL THE NEW POINTS Step 5 – Continue with other points

Reflecting across y-axis Refer to “Reflections” Worksheet Example #4 Pre-image Image C'(3, 7) C A T C’ C(-3, 7) A(-3, 2) A'(3, 2) A’ T’ T(2, 2) T'(-2, 2) What do you notice about the x and y coordinates of the pre-image and image points?

Reflecting across x-axis Reflect the following shape across the x-axis Pre-image Image M(2, 1) M’(2, -1) A(-1, 1) A’(-1, -1) T H T(-3, 5) T’(-3, -5) A M H(4, 5) H’(4, -5) A’ M’ T’ H’ What do you notice about the x and y coordinates of the pre-image and image points?

Reflecting across the line y = x Refer to “Reflections” Worksheet #6 Pre-Image Image F(-3, 0) F‘(0, -3) I(4, 0) I’ S’ I'(0, 4) S(4, -9) F I S'(-9, 4) F’ H(-3, -9) H'(-9, -3) H’ What do you notice about the x and y coordinates of the pre-image and image points? H S

If time permits, work on problem 8 on “Reflections” Worksheet. 8. Reflect across y = –x M(-5, 2) O(-2, 2) V(0, 6) E(-7, 6) E’ E V M’ M’(-2, 5) O’(-2, 2) V’(-6, 0) E’(-6, -7) M O O’ V’

If time permits, work on problem 7 on “Reflections” Worksheet. 8. Reflect across y = -3 H’(-12, 2) A’(7, -7) T’(2, -7) H T A

Reflect the rectangle with vertices S(3, 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). S(3, 4) S’(3, –4) V S U T T(3, 1) T’(3, –1) U(–2, 1) U’(–2, –1) V’ S’ U’ T’ V(–2, 4) V’(–2, –4) Graph the image and preimage.

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