splash screen. lesson menu five-minute check (over lesson 9–1) then/now new vocabulary key...
TRANSCRIPT
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
You found the magnitude and direction of vectors. (Lesson 8–7)
• Draw translations.
• Draw translations in the coordinate plane.
Draw a Translation
Copy the figure and given translation vector. Then draw the translation of the figure along the translation vector.
Step 2 Measure the length ofvector . Locate point G'by marking off this distancealong the line throughvertex G, starting at G andin the same direction as thevector.
Step 1 Draw a line through eachvertex parallel to vector .
Draw a Translation
Answer:
Step 3 Repeat Step 2 to locate points H', I', and J' toform the translated image.
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.
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:
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.
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:
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'.
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)
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.
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.
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:
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.
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