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