Five-Minute Check (over Lesson 9–1) CCSS Then/Now New Vocabulary Key Concept: Translation Example 1: Draw a Translation Key Concept: Translation in the Coordinate Plane Example 2: Translations in the Coordinate Plane Example 3: Real-World Example: Describing Translations Lesson Menu

Name the reflected image of BC in line m. ___ A. B. C. D. 5-Minute Check 1

Which of the following shows a reflection in the x-axis? A. B. C. D. 5-Minute Check 6

Which of the following shows a reflection in the x-axis? A. B. C. D. 5-Minute Check 6

Mathematical Practices 5 Use appropriate tools strategically. 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. Mathematical Practices 5 Use appropriate tools strategically. 4 Model with mathematics CCSS

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

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), N(4, 1), 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

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) 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) Example 2

B. Graph ΔGHJK 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 ΔG'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) Example 2

B. Graph ΔGHJK 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 ΔG'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) 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

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: 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

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: 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)) 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)) 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 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 Example 3