(8) Lesson 6.1 - Translations

1. Course 3, Lesson 6-1
Graph the ordered pairs. Then find the distance
between the points. Round to the nearest tenth if
necessary.
1. (1, 1), (3, 3) 2. (0, 4), (3, 2)
3. (–3, 2), (–1, –1) 4. (–1.5, –2), (0.5, 2)
5. Andy played a game with coordinates. Andy was at the
point (–10, –5). His opponent was at the point (10, 5).
What was the distance between Andy and his opponent?

2. Course 3, Lesson 6-1
ANSWERS
1. 2.8 units
2. 3.6 units
3. 3.6 units
4. 4.5 units
5. 22.4 units

3. HOW can we best show or describe the
change in position of a figure?
Geometry
Course 3, Lesson 6-1

4. Course 3, Lesson 6-1 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices
and Council of Chief State School Officers. All rights reserved.
Geometry
• 8.G.1
Verify experimentally the properties of rotations, reflections, and
translations.
• 8.G.3
Describe the effect of dilations, translations, rotations, and
reflections, on two-dimensional figures using coordinates.

5. Course 3, Lesson 6-1 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices
and Council of Chief State School Officers. All rights reserved.
Geometry
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
8 Look for and express regularity in repeated reasoning.

6. To
• translate a figure on the
coordinate plane
Course 3, Lesson 6-1
Geometry

7. Symbols
• transformation (x, y)  (x + a, y + b)
• preimage A’ is read A prime
• image
• translation
• congruent
Course 3, Lesson 6-1
Geometry

8. Course 3, Lesson 6-1
Geometry
Words When a figure is translated, the x-coordinate of the
preimage changes by the value of the horizontal
translation a. The y-coordinate of the preimage changes
by the vertical translation b.
Model
Symbols ( , ) ( , )x y x a y b  

9. 1
Need Another Example?
2
3
Step-by-Step Example
1. Graph JKL with vertices J(–3, 4), K(1, 3), and
L(–4, 1). Then graph the image of JKL after a
translation 2 units right and 5 units down. Write
the coordinates of its vertices.
Move each vertex of the triangle 2 units right and 5 units
down. Use prime symbols for the vertices of the image.
From the graph, the coordinates of the vertices of
the image are J'(–1, –1), K'(3, –2), and L'(–2, –4).

10. Answer
Need Another Example?
Graph ABC with vertices A(–2, 2), B(3, 4),
and C(4, 1). Then graph the image of ABC
after a translation 2 units left and 5 units
down. Write the coordinates of its vertices.
A'(–4, –3),
B'(1, –1),
C'(2, –4)

11. 1
Need Another Example?
2
3
Step-by-Step Example
2. Triangle XYZ has vertices X(–1, –2), Y(6, –3) and
Z(2, –5). Find the vertices of X'Y'Z' after a
translation of 2 units left and 1 unit up.
Use a table. Add –2 to the x-coordinates and 1 to
the y-coordinates.
So, the vertices of X'Y'Z' are X'(–3, –1), Y'(4, –2),
and Z'(0, –4).

12. Answer
Need Another Example?
Rectangle ABCD has vertices A(–3, 2),
B(2, 2), C(2, –3), and D(–3, –3). Find the
vertices of rectangle A'B'C'D' after a
translation of 4 units right and 2 units down.
A'(1, 0), B'(6, 0), C'(6, –5), D'(1, –5)

13. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. A computer image is being translated to create the
illusion of movement. Use translation notation to
describe the translation from point A to point B.
Point A is located at (3, 3). Point B is located at (2, 1).
(x, y) (x + a, y + b)
(3, 3) (3 + a, 3 + b) (2, 1)
3 + a = 2 3 + b = 1
a = –1 b = –2
So, the translation is (x – 1, y – 2), 1 unit to the left and
2 units down.

14. Answer
Need Another Example?
The character below was translated from
point A to point B. Use translation notation to
describe the translation.
(x – 2, y + 4)

15. How did what you learned
today help you answer the
HOW can we best show or describe the
change in position of a figure?
Course 3, Lesson 6-1
Geometry

16. How did what you learned
today help you answer the
HOW can we best show or describe the
change in position of a figure?
Course 3, Lesson 6-1
Geometry
Sample answers:
• You can use symbolic notation (x, y)  (x + a, y + b) to
describe the translation of a figure.
• You can graph the original figure and the image to
show the translation of a figure.

17. If point P(–3, 2) is
translated 3 units right
and 2 units down, what
are the coordinates of P'?
Course 3, Lesson 6-1
Ratios and Proportional RelationshipsFunctionsGeometry