Aim: Transformation: Reflection Course: Alg. 2 & Trig. Do Now: Aim: Let’s look at Reflections and ask ‘whuch u lookin’ at’?

Aim: Transformation: Reflection Course: Alg. 2 & Trig.

Do Now:

Aim: Let’s look at Reflections and ask ‘whuch u lookin’ at’?

3Find the inverse of 5.

4Is this a one-to-one function?

y x


Line Symmetry

A figure has LINE SYMMETRY if at least one line can be drawn through the

figure so that half of it is mirrored.

AT

Lines of symmetry or

reflection

Lines of symmetry or

reflection


Rotational Symmetry

Do either of these regular polygons have rotational symmetry? If so, how many degrees is required for each figure to coincide with the original?

A figure has ROTATIONAL SYMMETRY if the figure coincides with itself when it is

rotated 1800 or less in either direction.

Rotated 600, an regular hexagon will coincide

with the original.

1200

Rotated 1200, an equilateral triangle will

coincide with the original triangle

600


Point Symmetry

A figure has POINT SYMMETRY if the figure coincides with itself when it is rotated 1800 in either direction.

HH HHHH


Point & Line Symmetries

H

A

WOW


Reflection

Properties:•The Image is congruent to the Original• The Orientation of Image is reversed

(right is left and left is right)

Original Image

Lin

e of

R

efle

ctio

n

•The Line of Reflection is perpendicular to and bisects any segment connecting

corresponding points on the Image and the Original figure.


Reflections in Coordinate Geometry

C’ is the mirror image of C D’ is the mirror image of D E’ is the mirror image of E

C’ is the mirror image of C D’ is the mirror image of D E’ is the mirror image of E

m

DC’

D’C

E E’

Line m acts like a mirror and is called the LINE OF REFLECTION or

LINE OF SYMMETRY

Line m acts like a mirror and is called the LINE OF REFLECTION or

LINE OF SYMMETRY



• CDE is reflected in the y-axis• C’D’E’ is mirror image of CDE



P(3, 2)

What are the images of points P & S reflected through the y-axis? (ry)

y

x

S(1, 4)

What are the images of points P & S reflected through the x-axis?

P’(-3, 2)

S’(-1, 4)

S(1, 4) S’(-1, 4)

P”(3, -2)P(3, 2) P”(3, -2)

S”(1, -4)S(1, 4) S”(1, -4)

P(3, 2) P’(-3, 2)



P’(-x, y) P(x, y)

Under reflection in the y-axis (ry) , the Image of P(x, y) is P’(-x, y)

y

x

Under reflection in the x-axis, the Image of P(x, y) P"(x, -y)

P”(x, -y)

P(x, y) P’(-x, y)

P(x, y) P”(x, -y)


Reflections through the Origin

P’(-x, y) P(x, y)

Under reflection in the origin (ro) , the Image of P(x, y) is ?

y

x

Under reflection in the origin, the Image of P(x, y) P”(-x, -y)

P”(-x, -y)

What is the image of (-3,4) under a reflection in the origin? (3,-4)

(-3, 4)

(3, -4)


Reflections through the y = x

P(x, y)

Under reflection in y = x (ry = x) , the Image of P(x, y) is ?

y

x(3, 1)

P’(y, x)(1, 3) y =

x

Under reflection in the y = x, the Image of P(x, y) P’(y, x)

What is the image of (-3,4) under a reflection in y = x? (4,-3)


Model Problem

Plot ABC: A(-3, 1), B(-1, 5) and C(-2, -5).

Plot A’B’C’, the image of ABC under a reflection in the y-axis (ry) and write the coordinates. y

A(-3, 1)

B(-1, 5)

C(-2, -5)

A’(3, 1)

B’(1, 5)

C’(2, -5)


Model Problem

If the point (-4, -3) is reflected over the x-axis, what are the coordinates of the image?

If the point (2, -1) is reflected over x = 1, what are the coordinates of the image?

(2, -1)

x =

1

(-4, -3)

(0, -1)

(0, -1)

(-4, 3)

(-4, 3)


Model Problem

Plot ABC: A(0, 4), B(-3, 6) and C(-4, 2).Plot A’B’C’, the image of ABC under a reflection in the origin (rO) and write the coordinates.

yA(0,4)

B(-3,6)

C(–4,2)

A’(0,-4)B’(3, -6)

C’(4, -2)

Under reflection in the origin, the Image of P(x, y)

P”(-x, -y)


Model Problem

Documents

Aim: Transformation: Reflection Course: Alg. 2 & Trig. Do Now: Aim: Let’s look at Reflections and ask ‘whuch u lookin’ at’?