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Check 12-2 HW. Graphing Translation. 12-3. Course 1. 6 th Grade Math HOMEWORK. Page 629 #14-16. Tables and Functions. 12-1. Course 1. Our Learning Goal Students will understand functions by creating tables and graphing translations. Tables and Functions. 12-1. Course 1. - PowerPoint PPT Presentation
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Check 12-2 HW
Course 1
12-3 Graphing Translation
6th Grade Math HOMEWORK
Page 629
#14-16
Course 1
12-1 Tables and Functions
Our Learning GoalStudents will
understand functions by creating tables and graphing translations.
Course 1
12-1 Tables and Functions
Students will understand functions by creating tables and graphing translations.
• Learn to use data in a table to write an equation for a function and to use the equation to find a missing value.
• Learn to represent linear functions using ordered pairs and graphs.
• Learn to use translations to change the positions of figures on a coordinate plane.
• Learn to use reflections to change the positions of figures on a coordinate plane.
• Learn to use rotations to change positions of figures on a coordinate plane.
• Learn to visualize and show the results of stretching or shrinking a figure.
Today’s Learning Goal Assignment
Learn to use translations to change the positions of figures on a coordinate plane.
Course 1
12-3 Graphing Translation
12-3 Graphing Translations
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm Up
1. Use the given x-values to write solutions of the following equation as ordered pairs. y = 6x – 2 for x = 0, 1, 2, 3
2. Determine whether (3, –13) is a solution to the equation y = –4x – 1.
(0, –2), (1, 4), (2, 10), (3, 16)
yes
Course 1
12-3 Graphing Translation
Problem of the Day
Samantha’s house is 3 blocks east and 5 blocks south of Tyra. If Tyra walks straight south and then straight east to Samantha’s house, does she walk more blocks east or more blocks south? How many more?
south; 2 blocks
Course 1
12-3 Graphing Translation
A translation is a movement of a figure along a straight line. You can translate a figure on a coordinate plane by sliding it horizontally, vertically, or diagonally.
Course 1
12-3 Graphing Translation
Additional Example 1: Translating Figures on a Coordinate Plane
Give the coordinates of the vertices of the figure after the given translation.
Translate triangle DEF 4 units left and 3 units up.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
654321
-1-2-3-4-5-6
F
D
E
y
x
Course 1
12-3 Graphing Translation
Additional Example 1 Continued
To move the triangle 4 units left, subtract 4 from each of the x-coordinates.
To move the triangle 3 units up, add 3 to each of the y-coordinates.
DEF D’E’F’
D(1, 4)
E(4, 2)
F(–3, –3)
D’(1 – 4, 4 + 3) D’(–3, 7)
E’(0, 5)
F’(–7, 0)
E’(4 – 4, 2 + 3)
F’(-3 – 4, –3 + 3)
Course 1
12-3 Graphing Translation
Additional Example 1 Continued
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
543
1
-2-3
-5-6
6
2
-1
-4
E’
F’
D’ y
x
F
D
E
Course 1
12-3 Graphing Translation
Try This: Example 1
Give the coordinates of the vertices of the figure after the given translation.
Translate triangle GHJ 3 units left and 3 units up.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
654321
-1-2-3-4-5-6
J
G H
y
x
Course 1
12-3 Graphing Translation
Try This: Example 1
To move the triangle 3 units left, subtract 3 from each of the x-coordinates.
To move the triangle 3 units up, add 3 to each of the y-coordinates.
GHJ G’H’J’
G(2, 4)
H(4, 4)
J(–3, –2)
G’(2 – 3, 4 + 3) G’(–1, 7)
H’(1, 7)
J’(–6, 1)
H’(4 – 3, 4 + 3)
J’(–3 – 3, –2 + 3)
Course 1
12-3 Graphing Translation
Try This: Example 1 Continued
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
543
1
-2-3
-5-6
6
2
-1
-4
H’
J’
G’ y
x
J
G H
x
Course 1
12-3 Graphing Translation
Additional Example 2: Music Application
Members of a marching band begin in a trapezoid formation represented by trapezoid KLMN. Then they move 4 steps right and 5 steps down. Give the coordinates of the vertices of the trapezoid after such a translation.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
654321
-1-2-3-4-5-6
M
K L
y
x
N
-7-8
Course 1
12-3 Graphing Translation
Additional Example 2 Continued
To move 4 steps right, add 4 to each of the x-coordinates.
To move 5 steps down, subtract 5 from each of the y-coordinates.
KLMN K’L’M’N’
K(–2, 1)
L(1, 1)
M(3, –3)
K’(–2 + 4, 1 – 5) K’(2, –4)
L’(5, –4)
M’(7, –8)
L’(1 + 4, 1 – 5)
M’(3 + 4, –3 – 5)
N(–4, –3) N’(0, –8)M’(–4 + 4, –3 – 5)
Course 1
12-3 Graphing Translation
Additional Example 2 Continued
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
654321
-1-2-3-4-5-6
M
K L
y
x
N
-7 M’
K’ L’
N’-8
x
Course 1
12-3 Graphing Translation
Try This: Example 2
Members of a flag team begin in a trapezoid formation represented by trapezoid KLMN. Then they move 3 steps right and 2 steps down. Give the coordinates of the vertices of the trapezoid after such a translation.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
654321
-1-2-3-4-5-6
M
K L
y
x
N
Course 1
12-3 Graphing Translation
Try This: Example 2
To move 3 steps right, add 3 to each of the x-coordinates.
To move 2 steps down, subtract 2 from each of the y-coordinates.
KLMN K’L’M’N’
K(–1, 3)
L(1, 3)
M(3, –1)
K’(–1 + 3, 3 – 2) K’(2, 1)
L’(4, 1)
M’(6, –3)
L’(1 + 3, 3 – 2)
M’(3 + 3, –1 – 2)
N(–3, –1) N’(0, –3)M’(-3 + 3, –1 – 2)
Course 1
12-3 Graphing Translation
Try This: Example 2 Continued
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
654321
-1-2-3-4-5-6
M
K L
y
N
x
M’
K’ L’
N’
Course 1
12-3 Graphing Translation
Lesson Quiz
Give the coordinates of the vertices of triangle ABC, with vertices A(-5, -4), B(-3, 2), and C(1, -3), after the given translations.
1. Translate triangle ABC 3 units up and 2 units
right.
2. Translate triangle ABC 5 units down and 3 units
left.
3. Translate triangle ABC 2 units down and 4 units
right.
A’(-3, -1), B’(-1, 5), and C’(3,0)
Insert Lesson Title Here
A’(-8, -9), B’(-6, -3), and C’(-2,-8)
A’(-1, -6), B’(1, 0), and C’(5,-5)
Course 1
12-3 Graphing Translation