9 2 Translations Warm Up Find the coordinates

9 -2 Translations 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 Holt Mc. Dougal Geometry

9 -2 Translations Objective Identify and draw translations. Holt Mc. Dougal Geometry

9 -2 Translations 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. Holt Mc. Dougal Geometry

9 -2 Translations Example 1: Identifying Translations Tell whether each transformation appears to be a translation. Explain. A. No; the figure appears to be flipped. Holt Mc. Dougal Geometry B. Yes; the figure appears to slide.

9 -2 Translations 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. Holt Mc. Dougal Geometry

9 -2 Translations 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. Holt Mc. Dougal Geometry

9 -2 Translations 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. Holt Mc. Dougal Geometry

9 -2 Translations Holt Mc. Dougal Geometry

9 -2 Translations 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). D(– 3, – 1) D’(– 3 + 3, – 1) = D’(0, – 2) E(5, – 3) E’(5 + 3, – 3 – 1) = E’(8, – 4) F(– 2, – 2) F’(– 2 + 3, – 2 – 1) = F’(1, – 3) Graph the preimage and the image. Holt Mc. Dougal Geometry

9 -2 Translations 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). R(2, 5) R’(2 – 3, 5 – 3) = R’(– 1, 2) S(0, 2) S’(0 – 3, 2 – 3) = S’(– 3, – 1) T(1, – 1) T’(1 – 3, – 1 – 3) = T’(– 2, – 4) U(3, 1) U’(3 – 3, 1 – 3) = U’(0, – 2) Graph the preimage and the image. Holt Mc. Dougal Geometry R R’ S S’ U’ T’ U T

9 -2 Translations Assignment Pg. 614 (2 -22 even) Holt Mc. Dougal Geometry