Splash Screen

Lesson Menu Five-Minute Check (over Lesson 9–1) 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

Over Lesson 9–1 5-Minute Check 1 Name the reflected image of BC in line m. ___ A. B. C. D.

Over Lesson 9–1 5-Minute Check 2 Name the reflected image of AB in line m. ___ A. B. C. D.

Over Lesson 9–1 5-Minute Check 3 A.ΔFGE B.ΔEGD C.ΔCGD D.ΔBCG Name the reflected image of ΔAGB in line m.

Over Lesson 9–1 5-Minute Check 4 A.D B.E C.F D.G Name the reflected image of B in line m.

Over Lesson 9–1 5-Minute Check 5 A.AFEB B.DCBE C.EDCF D.FEDA Name the reflected image of ABCF in line m.

Over Lesson 9–1 5-Minute Check 6 Which of the following shows a reflection in the x-axis? A.B. C.D.

Then/Now You found the magnitude and direction of vectors. (Lesson 8–7) Draw translations. Draw translations in the coordinate plane.

Vocabulary translation vector

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 2Measure 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. Step 1Draw a line through each vertex parallel to vector.

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

Example 1 Which of the following shows the translation of ΔABC along the translation vector? A.B. C.D.

Concept

Example 2 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 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 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.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. 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'.

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)

Example 3 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: 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=0b=–3 Answer: translation vector:

Example 3 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. 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.

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 

End of the Lesson