Lesson 19
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
Period:________ Date:_________
M1
GEOMETRY
Lesson 19 - Translations on the Coordinate Plane
Learning Targets I can draw the translation of a given figure on the coordinate plane
Definitions- Vocabulary


A translation is a ____________________ transformation where all the points of a figure are moved
the same ______________ in the same __________________.
A translation is an _______________, so the image of a translated figure is congruent to the preimage.
Translation is a " ______________________" Coordinates change : ______________________
Example 1) In the figure to the right, quadrilateral 𝐴𝐵𝐶𝐷 has been translated
⃗⃗⃗⃗⃗⃗ .
the length and direction of vector 𝐶𝐶′
⃗⃗⃗⃗⃗⃗⃗ .
Draw vectors ⃗⃗⃗⃗⃗⃗
𝐴𝐴′ and 𝐵𝐵′
Notice that the distance and direction from each vertex to its corresponding
⃗⃗⃗⃗⃗⃗ .
vertex on the image are identical to that of 𝐶𝐶′
Properties of Translations: For vector ⃗⃗⃗⃗⃗
𝐴𝐵 , the translation along ⃗⃗⃗⃗⃗
𝐴𝐵 is the transformation 𝑇⃗⃗⃗⃗⃗
𝐴𝐵 of the plane as
defined as follows:
Example 2) Draw the vector that defines each translation below.
Example 3. Translate the image one unit down and three
units right. Draw the vector that defines the translation.
Lesson 19
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
Period:________ Date:_________
M1
GEOMETRY
Translations and vectors:
The translation at the right shows a vector translating the top
triangle 4 units to the right and 9 units downward.
The notation for such vector movement may be written as:
〈4, −9〉
_______________
________________
Example 4 Write a rule to describe the translation.
Explain why 𝐴𝐵𝐶𝐷 ≅ 𝐴’𝐵’𝐶’𝐷’
Example 5. 𝛥𝑋𝑌𝑍 has coordinates 𝑋(8, 3), 𝑌(1, 4), 𝑎𝑛𝑑 𝑍(8, 9). A translation maps 𝑋 to 𝑋′(4, 8). What are
the coordinates for 𝑌′ and 𝑍′ for this translation?
Hint:
𝑽𝒆𝒄𝒕𝒐𝒓 = 𝑻𝑶 − 𝑭𝑹𝑶𝑴
Try on your own
Example 4. State the coordinates of ∆𝐴𝐵𝐶. Then, graph the image of ∆𝐴𝐵𝐶 under the translation 𝑇−1,2 .
State the coordinates of the image.
𝐴: ______________________________
𝐵: ______________________________
𝐶: ______________________________
𝐴′: _____________________________
𝐵′: _____________________________
𝐶′: _____________________________
Lesson 19
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
Period:________ Date:_________
M1
GEOMETRY
Lesson 19 - Translations on the Coordinate Plane
Classwork
Translate each figure according to the instructions provided.
1) 2 units down and 3 units left.
Draw the vector that defines the translation.
2)
1 unit up and 2 units right.
Draw the vector that defines the translation.
3. Use the rule (𝑥, 𝑦)  (𝑥 + 7, 𝑦– 1) to find the translation image of 𝐿𝑀𝑁.
 Graph the image as 𝐿’𝑀’𝑁’ and state the new coordinates.
 State the rule in standard translation notation.
Lesson 19
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
Period:________ Date:_________
M1
GEOMETRY
Translations:
Graph the image of each figure under the given translation.
4.
𝑇<–1,4> ∶ (𝛥𝐴𝐵𝐶)
5.
𝑇<3,−3> ∶ (𝐽𝐾𝐿𝑀)
6. If 𝑇<10,7> ∶ (𝑄𝑅𝑆𝑇) = 𝑄′𝑅′𝑆′𝑇’, what translation maps 𝑄′𝑅′𝑆′𝑇’ onto 𝑄𝑅𝑆𝑇?
7. 𝛥𝑋𝑌𝑍 has coordinates 𝑋(2, 3), 𝑌(1, 4), 𝑎𝑛𝑑 𝑍(8, 9). A translation maps 𝑋 to 𝑋′(4, 8). What are the
coordinates for 𝑌′ and 𝑍′ for this translation?
8.
Write three different translation rules for which the image of 𝛥𝐴𝐵𝐶 has a vertex at the origin.
Lesson 19
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
Period:________ Date:_________
Lesson 19 - Translations on the Coordinate Plane
Homework
Graph the image of each figure under the given translation.
1.
𝑇<3,−2> : (𝛥𝐷𝐸𝐹)
3. Write a rule to describe the translation.
2. 𝑇<−4,0> : (𝑊𝑋𝑌𝑍)
M1
GEOMETRY
Lesson 19
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
4.
Period:________ Date:_________
M1
GEOMETRY
If 𝑇<−4,9>: (𝛥𝐿𝑀𝑁) = 𝛥𝐿’𝑀’𝑁’, what translation maps 𝛥𝐿’𝑀’𝑁’ onto 𝛥𝐿𝑀𝑁?
5. Use the rule (𝑥, 𝑦)  (𝑥 + 4, 𝑦 – 2) to find the translation image of 𝐿𝑀𝑁.
a. Graph the image as 𝐿’𝑀’𝑁’ and state the new coordinates.
b. State the rule in standard translation notation.
6. State the coordinates of ∆𝐴𝐵𝐶. Then, graph the image of ∆𝐴𝐵𝐶 under the translation 𝑇−2,−3.
7. Write one translation rule that is equivalent to the composite transformation of 𝑇−2,−3 followed by
𝑇5,−1.