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
Over Lesson 9–1
Name
___ the reflected image
of BC in line m.
A.
B.
C.
D.
Over Lesson 9–1
Name
___ the reflected image
of AB in line m.
A.
B.
C.
D.
Over Lesson 9–1
Name the reflected image
of ΔAGB in line m.
A. ΔFGE
B. ΔEGD
C. ΔCGD
D. ΔBCG
Over Lesson 9–1
Name the reflected image
of B in line m.
A. D
B. E
C. F
D. G
Over Lesson 9–1
Name the reflected image
of ABCF in line m.
A. AFEB
B. DCBE
C. EDCF
D. FEDA
Over Lesson 9–1
Which of the following shows a reflection in the
x-axis?
A.
B.
C.
D.
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
You found the magnitude and direction of
vectors.
• Draw translations.
• Draw translations in the coordinate plane.
• translation 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.
Draw a Translation
Step 3
Answer:
Repeat Step 2 to locate points H', I', and J' to
form the translated image.
Which of the following shows the translation
of ΔABC along the translation vector?
A.
B.
C.
D.
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. 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)
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)
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
Answer: translation vector:
b = –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))
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