Concept

Step 1 Draw a line through each vertex parallel to vector . 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: Example 1

Which of the following shows the translation of the figure ABCD along the translation vector? Example 1

Concept

Translations in the Coordinate Plane A. Graph ΔTUV with vertices T(–1, –4), U(6, 2), and V(5, –5) along the vector –3, 2. Example 2

The vector indicates a translation 3 units left and 2 units up. Translations in the Coordinate Plane The vector indicates a translation 3 units left and 2 units up. (x, y) → (x – 3, y + 2) T(–1, –4) → (–4, –2) U(6, 2) → (3, 4) V(5, –5) → (2, –3) Answer: Example 2

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

The vector indicates a translation 5 units left and 1 unit down. 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 2

A. 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) A B C D Example 2

B. Graph □GHJK with the vertices G(–4, –2), H(–4, 3), J(1, 3), K(1, –2) along the vector 2, –2. Choose the correct coordinates for □G'H'J'K'. A. G'(–6, –4), H'(–6, 1), J'(1, 1), K'(1, –4) B. G'(–2, –4), H'(–2, 1), J'(3, 1), K'(3, –4) C. G'(–2, 0), H'(–2, 5), J'(3, 5), K'(3, 0) D. G'(–8, 4), H'(–8, –6), J'(2, –6), K'(2, 4) A B C D Example 2

Describing Translations A. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 2 to position 3 in function notation and in words. Example 3

Answer: function notation: (x, y) → (x – 2, y – 3) Describing Translations The raindrop in position 2 is (1, 2). In position 3, this point moves to (–1, –1). Use the translation function (x, y) → (x + a, y + b) to write and solve equations to find a and b. (1 + a, 2 + b) or (–1, –1) 1 + a = –1 2 + b = –1 a = –2 b = –3 Answer: function notation: (x, y) → (x – 2, y – 3) So, the raindrop is translated 2 units left and 3 units down from position 2 to 3. Example 3

Answer: translation vector: Describing Translations B. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 3 to position 4 using a translation vector. (–1 + a, –1 + b) or (–1, –4) –1 + a = –1 –1 + b = –4 a = 0 b = –3 Answer: translation vector: Example 3

A. The graph shows repeated translations that result in the animation of the soccer ball. Choose the correct translation of the soccer ball from position 2 to position 3 in function notation. A. (x, y) → (x + 3, y + 2) B. (x, y) → (x + (–3), y + (–2)) C. (x, y) → (x + (–3), y + 2) D. (x, y) → (x + 3, y + (–2)) A B C D Example 3

B. The graph shows repeated translations that result in the animation of the soccer ball. Describe the translation of the soccer ball from position 3 to position 4 using a translation vector. A. –2, –2 B. –2, 2 C. 2, –2 D. 2, 2 A B C D Example 3