4-2 Unit 4 Transformations

4-2 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. 4-2 Every transformation has a pre-image and an image. Pre-image is the original figure in the transformation (the “before”). Image is the shape that results from the transformation (the “after”).

4-2 Example Pre-Image Image A' A B B' C' C

4-2 Mapping A way of showing where you started and finished a transformation. It uses an arrow (→) Arrow is a sign for transformation.

Remember equations for horizontal lines: 4-2 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: 4-2 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 - Reflection happens across a line of reflection . 4-2 12-1 Reflections - Reflection happens across a line of reflection . - Reflect a figure across vertical, horizontal or oblique line - Across the x-axis, the y-axis the line y = x, or the line y = –x Holt Geometry

4-2 Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line.

Example 1: Identifying Reflections 4-2 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..

4-2 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.

4-2

4-2

4-2

Reflecting across vertical lines (x = a) 4-2 Reflecting across vertical lines (x = a) 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 4-2 Reflecting across y-axis 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 4-2 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 4-2 Reflecting across the line y = x 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

4-2

4-2 8. Reflect across y = –x M(-5, 2) O(-2, 2) V(0, 6) E(-7, 6)

4-2

Reflect the rectangle with vertices S(3, 4), 4-2 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.

4-2 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)

4-2 CW 4-2 Q# 5,7,8,10,11,13,14,17,18,19

4-2 Solutions for CW 4-2