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Lesson 10-9 Pages 456-459
Reflections
What you will learn!
How to identify figures with line symmetry and graph reflections on a
coordinate plane.
Line SymmetryLine SymmetryLine of symmetryLine of symmetryReflectionReflection
What you really need to know!
What you really need to know!
A type of transformation where a figure is flipped over a line of symmetry is a reflection.
What you really need to know!To draw the reflection of a polygon, find the distance from each vertex of the polygon to the line of symmetry. Plot the new vertices the same distance from the line of symmetry but on the other side of the line. Then connect the new vertices to complete the reflected image.
Example 1:
Determine whether each figure has a line of symmetry. If so, copy the figure and draw all the lines of symmetry.
Example 2:
Determine whether each figure has a line of symmetry. If so, copy the figure and draw all the lines of symmetry.
Example 3:
Determine whether each figure has a line of symmetry. If so, copy the figure and draw all the lines of symmetry.
No symmetry
Example 4:
Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph the figure and its reflected image.
R
Q
S
T
R’
Q’
S’
T’
Q (-1,1)
R (0,3)
S (3,2)
T (4,0)
Q’ (-1,-1)
R’ (0,-3)
S’ (3,-2)
T’ (4,0)
Vertices ofVertices ofQuadrilateral Quadrilateral QRSTQRST
DistanceDistancefrom from xx--
axisaxis
Vertices ofVertices ofQuadrilateral Quadrilateral
QQRRSSTT
QQ(–1, 1)(–1, 1) 11 Q’ (-1,-1)Q’ (-1,-1)RR(0, 3)(0, 3) 33 R’ (0,-3)R’ (0,-3)SS(3, 2)(3, 2) 22 S’ (3,-2)S’ (3,-2)TT(4, 0)(4, 0) 00 T’ (4,0)T’ (4,0)
Example 5:
Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2).
Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image.
X
Y
Z
Y’
X’
Z’
X (1,2)
Y (2,1)
Z (1,-2)
X’ (-1,2)
Y’ (-2,1)
Z’ (-1,-2)
Vertices of Vertices of XYZXYZ
DistanceDistancefrom from yy-axis-axis
Vertices ofVertices ofXXYYZZ
XX(1, 2)(1, 2) 11 X’ (-1,2)X’ (-1,2)YY(2, 1)(2, 1) 22 Y’ (-2,1)Y’ (-2,1)ZZ(1, –2)(1, –2) 11 Z’ (-1,-2)Z’ (-1,-2)
Page 458
Guided Practice
#’s 3-6
A (5,8)
B (1,2)
C (6,4)
W (-4,-2)
X (-4,-3)
Y (-2,4)
Z (-2,-1)
Pages 456-457 with someone at home and study
examples!
Read:
Homework: Page 458-459
#’s 7-17 all
#’s 20-27 all
Lesson Check Ch 10
F
E
D (-3,6)
E (-2,-3)
F (2,2)
G (4,9)
T
U V
T’
U’ V’
T (-6,1)
U (-2,-3)
V (5,-4)
Q (2,-5)
R (4,-5)
S (2,3)
Q’ (-2,-5)
R’ (-4,-5)
S’ (-2,3)
H
I
J
K
J’
I’
H’
K’
H (-1,3)
I (-1,-1)
J (2,-2)
K (2,2)
H’ (1,3)
I’ (1,-1)
J’ (-2,-2)
K’ (-2,2)
Study Guide and Review
Pages
462-464
#’s 6-22(Odd answers in back of book)
Prepare for Test!
Page
465
#’s 1-16
Prepare for Test!
Pages
466-467
#’s 1-17
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