Five-Minute Check (over Lesson 3–1) Mathematical Practices 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

What is coordinate of the image of the point (–5, 2) after a reflection in the line y = x? B. (–5, –2) C. (5, –2) D. (5, 2) 5-Minute Check 2

(x, y)  (–x, y) reflection in the y-axis Mateo draws a rectangle with vertices A(−3, 2), B(–3, 5), C(4, 5), and D(4, 2), and then its reflection at A′(−3, –2), B′(–3, –5), C′(4, –5), and D′(4, –2). Describe the transformation using coordinate notation. (x, y)  (–x, y) reflection in the y-axis (x, y)  (x, –y) reflection in the x-axis C. (x, y)  (y, x) reflection in the line y = x D. (x, y)  (–y, –x) reflection in the line y = –x 5-Minute Check 3

Triangle JKL has vertices J(–4, 2)), K(–1, 5), and L(–1, 1) Triangle JKL has vertices J(–4, 2)), K(–1, 5), and L(–1, 1). What are the coordinates of the image of vertex K after a refection in the line x = 2? A. K’(1, 5) B. K’(3, 5) C. K’(5, 1) D. K’(5, 5) 5-Minute Check 4

Which of the following is the image of the line y = 2x – 3 under the reflection (x, y)  (–x, y)? A. y = 2x + 3 B. y = –2x – 3 C. y = –2x + 3 D. y = 3x – 3 5-Minute Check 5

Mathematical Practices 5 Use appropriate tools strategically. 7 Look for and make use of structure. 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. G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. MP

You found the magnitude and direction of vectors. Draw translations. Draw translations in the coordinate plane. Then/Now

translation vector Vocabulary

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 ΔABC along the translation vector? C. D. 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), 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

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

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)) 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