Translations 9.2 Content Standards G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Concept

Example 1 Draw a Translation Copy the figure and given translation vector. Then draw the translation of the figure along the translation vector. Step 1 Draw a line through each vertex parallel to vector . Step 2 Measure the length of vector . Locate point G' by marking off this distance along the line through vertex G, starting at G and in the same direction as the vector.

Example 1 Draw a Translation Step 3 Repeat Step 2 to locate points H', I', and J' to form the translated image. Answer:

Concept

Example 2 Translations in the Coordinate Plane Graph pentagon PENTA with vertices P(1, 0), E(2, 2), N(4, 1), T(4, –1), and A(2, –2) along the vector –5, –1.

Example 2 Translations in the Coordinate Plane The vector indicates a translation 5 units left and 1 unit down. (x, y) → (x – 5, y – 1) P(1, 0) → (–4, –1) E(2, 2) → (–3, 1) N(4, 1) → (–1, 0) T(4, –1) → (–1, –2) A(2, –2) → (–3, –3) Answer:

Example 3 Graph ΔABC with the vertices A(–3, –2), B(4, 4), C(3, –3) along the vector –1, 3. Choose the correct coordinates for ΔA'B'C'. A. A'(–2, –5), B'(5, 1), C'(4, –6) B. A'(–4, –2), B'(3, 4), C'(2, –3) C. A'(3, 1), B'(–4, 7), C'(1, 0) D. A'(–4, 1), B'(3, 7), C'(2, 0)