lesson 10-8 pages 451-454 translations. what you will learn! how to graph translations of polygons...
TRANSCRIPT
Lesson 10-8 Pages 451-454
Translations
What you will learn!
How to graph translations of polygons on a coordinate plane.
TransformationTransformationTranslationTranslation
What you really need to know!
A translation is the movement of a geometric figure in some direction without turning the figure. When translating a figure, every point of the original figure is moved the same distance and in the same direction.
What you really need to know!
To graph a translation of a figure, move each vertex of the figure in the given direction. Then connect the new vertices.
Example 1:
Translate ∆ABC 5 units left and 1 unit up.
B
CA
A’
B’
C’
A (1,-3)
B (4,1)
C (5,-3)
A’ (-4,-2)
B’ (-1,2)
C’ (0,-2)
Example 2:
Trapezoid GHIJ has vertices G(–4, 1), H(–4, 3), I(–2, 3), and J(–1, 1). Find the vertices of trapezoid GHIJ after a translation of 5 units right and 3 units down. Then graph the figure and its translated image.
G
H I
J
G'
H' I'
J'
G (-4,1)
H (-4,3)
I (-2,3)
J (-1,1)
G’ (1,-2)
H’ (1,0)
I’ (3,0)
J’ (4,-2)
Vertices of trapezoid Vertices of trapezoid GHIJGHIJ
((xx + 5, + 5, yy – 3) – 3) Vertices of trapezoid Vertices of trapezoid GGHHIIJJ
GG(–4, 1)(–4, 1)
HH(–4, 3)(–4, 3)
II(–2, 3)(–2, 3)
JJ(–1, 1)(–1, 1)
(–4 + 5, 1 – 3) G(1, –2)
(–4 + 5, 3 – 3) H(1, 0)
(–2 + 5, 3 – 3) I(3, 0)
(–1 + 5, 1 – 3) J(4, –2)
Example 3: Ana is seated at the square marked X. She is moved to the seat marked Y. Describe the translation as an ordered pair.
(2,2)
Page 453
Guided Practice
#’s 3-5
A'
C'
B'
A (2,6)
B (4,2)
C (1,3)
A’ (-1,3)
B’ (1,-1)
C’ (-2,0)
D (1,0)
E (-2,-2)
F (2,4)
G (6,-3)
D’ (5,-5)
E’ (2,-7)
F’ (6,-1)
G’ (10,-8)
D (1,0)
E (-2,-2)
F (2,4)
G (6,-3)
D (7,0)
E (4,-2)
F (8,4)
G (12,-3)
Pages 451-452 with someone at home and study
examples!
Read:
Homework: Page 453-454
#’s 6-13 all
#’s 19-26 all
Lesson Check 10-8
H(-1,0)
I (1,-3)
J (-2,-4)
H(1,-6)
I (3,-9)
J (0,-10)
K(1,-1)
L (1,1)
M (5,1)
N (5,-1)
K(0,2)
L (0,4)
M (4,4)
N (4,2)
P(0,0)
Q (5,-2)
R (-3,6)
P(0,0)
Q (5,-2)
R (-3,6)
P(0,0)
Q (5,-2)
R (-3,6)
P(0,0)
Q (5,-2)
R (-3,6)
Page
589
Lesson 10-8