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Reflections and Translations: Finding Coordinates

Practice finding the coordinates of the image of triangle ABC after reflection across the x-axis, y-axis, and a given line. Also, learn about translations and how to draw them. Includes examples and exercises.

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Reflections and Translations: Finding Coordinates

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  1. Warm Up Find the coordinates of the image of ∆ABC with vertices A(3, 4), B(–1, 4), and C(5, –2), after each reflection. 1. across the x-axis 2. across the y-axis 3. across the line y = x

  2. Objective Identify and draw translations.

  3. A translation is a transformation where all the points of a figure are moved the same distance in the same direction. A translation is an isometry, so the image of a translated figure is congruent to the preimage.

  4. Example 1: Identifying Translations Tell whether each transformation appears to be a translation. Explain. A. B. No; the figure appears to be flipped. Yes; the figure appears to slide.

  5. Example 2: Drawing Translations Copy the quadrilateral and the translation vector. Draw the translation along Step 1 Draw a line parallel to the vector through each vertex of the triangle.

  6. Example 2 Continued Step 2 Measure the length of the vector. Then, from each vertex mark off the distance in the same direction as the vector, on each of the parallel lines. Step 3 Connect the images of the vertices.

  7. A vector in the coordinate plane can be written as <a, b>, where a is the horizontal change and b is the vertical change from the initial point to the terminal (end) point.

  8. D(–3, –1) D’(–3 + 3, –1 – 1) = D’(0, –2) E(5, –3) E’(5 + 3, –3 – 1) = E’(8, –4) Example 3: Drawing Translations in the Coordinate Plane Translate the triangle with vertices D(–3, –1), E(5, –3), and F(–2, –2) along the vector <3, –1>. The image of (x, y) is (x + 3, y – 1). F(–2, –2) F’(–2 + 3, –2 – 1) = F’(1, –3) Graph the preimage and the image.

  9. R(2, 5) R’(2 – 3, 5 – 3) = R’(–1, 2) R S R’ S(0, 2) S’(0 – 3, 2 – 3) = S’(–3, –1) U S’ T(1, –1) T’(1 – 3, –1 – 3) = T’(–2, –4) T U’ U(3, 1) U’(3 – 3, 1 – 3) = U’(0, –2) T’ Check It Out! Example 3 Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,–1), and U(3, 1) along the vector <–3, –3>. The image of (x, y) is (x – 3, y – 3). Graph the preimage and the image.

  10. Assignment Pg. 614 (2-22 even)

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