Reflections
Reflections
Warm Up
Lesson Presentation
HoltMcDougal
Holt GeometryGeometry
Reflections
Warm-up
1. X +3 =10
2. 3x -5 =13
3. 2x -7 = 11
Holt McDougal Geometry
Reflections
Objective
Identify and draw reflections.
Holt McDougal Geometry
Reflections
Vocabulary
transformation reflection
preimage rotation
image translation
isometry
Holt McDougal Geometry
The Alhambra, a 13th-century palace in Grenada, Spain,
Reflections
is famous for the geometric patterns that cover its walls
and floors. To create a variety of designs, the builders
based the patterns on several different transformations.
A transformation is a change in the position, size, or
shape of a figure. The original figure is called the
preimage. The resulting figure is called the image. A
transformation maps the preimage to the image. Arrow
notation (→) is used to describe a transformation, and
primes (’) Geometry
Holt McDougal are used to label the image.
Reflections
Holt McDougal Geometry
Reflections
Example 1:
Preimage:DEFG
Image: D’E’F’G’
Holt McDougal Geometry
Reflections
Example 2:
Preimage:ABC
Image: A’B’C’
Holt McDougal Geometry
Reflections
Holt McDougal Geometry
Reflections
An isometry is a transformation that does not
change the shape or size of a figure. Reflections,
translations, and rotations are all isometries.
Isometries are also called congruence
transformations or rigid motions.
Recall that a reflection is a transformation that
moves a figure (the preimage) by flipping it across
a line. The reflected figure is called the image. A
reflection is an isometry, so the image is always
congruent to the preimage.
Holt McDougal Geometry
Reflections
Holt McDougal Geometry
Reflections
Example 3: Identifying Reflections
Tell whether each transformation appears to
be a reflection. Explain.
A. B.
No; the image does not Yes; the image appears
Appear to be flipped. to be flipped across a
line..
Holt McDougal Geometry
Reflections
Check It Out! Example 4
Tell whether each transformation appears to
be a reflection.
a. b.
No; the figure Yes; the image
does not appear to appears to be
be flipped. flipped across a line.
Holt McDougal Geometry
Reflections
Holt McDougal Geometry
Reflections
Check It Out! Example 5
Reflect the rectangle with vertices S(3, 4),
T(3, 1), U(–2, 1) and V(–2, 4) across the x-axis.
The reflection of (x, y) is (x,–y).
S(3, 4) S’(3, –4) V S
T(3, 1) T’(3, –1)
U(–2, 1) U’(–2, –1) U T
U’ T’
V(–2, 4) V’(–2, –4)
Graph the image and preimage. S’
V’
Holt McDougal Geometry
Reflections
Example 6: Drawing Reflections in the Coordinate
Plane
Reflect the figure with the given vertices
across the given line.
X(2, –1), Y(–4, –3), Z(3, 2); x-axis
The reflection of (x, y) is (x,–y). Y’
X(2,–1) X’(2, 1) Z
X’
Y(–4,–3) Y’(–4, 3)
X
Z(3, 2) Z’(3, –2) Z’
Y
Graph the image and preimage.
Holt McDougal Geometry
Reflections
Example 7: Drawing Reflections in the Coordinate
Plane
Reflect the figure with the given vertices
across the given line.
R(–2, 2), S(5, 0), T(3, –1); y = x
S’
The reflection of (x, y) is (y, x).
R(–2, 2) R’(2, –2) T’
R
S(5, 0) S’(0, 5)
S
T(3, –1) T’(–1, 3)
T
Graph the image and preimage. R’
Holt McDougal Geometry
Reflections
Example8: Drawing Reflections in the
Coordinate Plane
Reflect the figure with the given vertices
across the given line.
R(3, 3), S(4, 1), T(-2, -2);
x=1
Graph the image.
Holt McDougal Geometry
Reflections
Example9: Drawing Reflections in the
Coordinate Plane
Reflect the figure across the given line; y=-1.
Graph the image and state
the coordinates.
Holt McDougal Geometry
Reflections
Homework: Handout on Reflections
Holt McDougal Geometry
Reflections
Lesson Quiz: Part I
1. Tell whether the transformation appears to be a
reflection.
yes
2. Copy the figure and the line of reflection. Draw the
reflection of the figure across the line.
Holt McDougal Geometry
Reflections
Lesson Quiz: Part II
Reflect the figure with the given vertices
across the given line.
3. A(2, 3), B(–1, 5), C(4,–1); y = x
A’(3, 2), B’(5,–1), C’(–1, 4)
4. U(–8, 2), V(–3, –1), W(3, 3); y-axis
U’(8, 2), V’(3, –1), W’(–3, 3)
5. E(–3, –2), F(6, –4), G(–2, 1); x-axis
E’(–3, 2), F’(6, 4), G’(–2, –1)
Holt McDougal Geometry
