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Published byAsher Baker Modified over 6 years ago

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**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.

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

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**Which of the transformations are examples of**

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

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**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

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

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

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**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.

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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.

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**We are going to reflect images on the coordinate plane across given lines **

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**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 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.

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**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.

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**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.

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**F'( , ) I'( , ) S'( , ) H'( , ) Reflecting across the line y = x**

Remember: Move ONLY vertically or horizontally…think about why? Pre-Image Image F( , ) F'( , ) I( , ) I'( , ) F I S( , ) S'( , ) H( , ) H'( , ) H S Do #6 on your worksheet Label the coordinates of the preimage.

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**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?

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**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.

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**Reflect across y = –x C’( , ) A’( , ) K’( , ) E’( , )**

Do #8 on your worksheet

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**Reflect the figure with the given vertices across the given line.**

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)

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