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NAME ______________________________________________ DATE
9-1
____________ PERIOD _____
Practice
Reflections
Draw the image of each figure under a reflection in line ᐉ.
2.
ᐉ
ᐉ
COORDINATE GEOMETRY Graph each figure and its image under the given
reflection.
3. quadrilateral ABCD with vertices
A(⫺3, 3), B(1, 4), C(4, 0), and
D(⫺3, ⫺3) in the origin
4. 䉭FGH with vertices F(⫺3, ⫺1), G(0, 4),
and H(3, ⫺1) in the line y ⫽ x
y
x
O
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
y
5. rectangle QRST with vertices Q(⫺3, 2),
R(⫺1, 4), S(2, 1), and T(0, ⫺1)
in the x-axis
6. trapezoid HIJK with vertices H(⫺2, 5),
I(2, 5), J(⫺4, ⫺1), and K(⫺4, 3)
in the y-axis
y
O
x
O
y
x
x
O
ROAD SIGNS Determine how many lines of symmetry each sign has. Then
determine whether the sign has point symmetry.
7.
Chapter 9
8.
9.
9
Glencoe Geometry
Lesson 9-1
1.
NAME ______________________________________________ DATE
9-1
____________ PERIOD _____
Word Problem Practice
Reflections
1. REFLECTIONS Vincent is making a star
with a horizontal line of symmetry.
Complete the star by drawing the
reflected image of the figure over line m.
Table
4. INTERIOR DESIGN Wilfred hired an
interior designer to layout the furniture
in his bedroom. The designer produced
the plan shown in the figure.
Unfortunately,
Lamp
Wilfred’s
Desk
window is
located on the
opposite wall
Bed
from the plan.
Wilfred
decides to just
reflect the
plan over the
vertical line through the center of the
room. Draw the reflected plan.
Window
m
Bureau
2. LINES OF SYMMETRY Maria placed a
paper cutout on a table and then left to
get some glue. Her friend James flipped
over the cutout without telling Maria.
Still, when Maria came back it was
impossible for her to be able to see that
anything had been changed. Draw a line
through the figure that represents the
line over which James must have flipped
the figure.
y
3. SYMMETRY Martha made the figure
shown. How many lines of symmetry
does the figure have?
5
O
5
x
5. What are the vertices of the image of
this triangle if it is reflected over the yaxis?
6. What are the vertices of the image of
this triangle if it is reflected over the
line y = x?
Chapter 9
10
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
TRIANGLES For Exercises 5 and 6, use
the following information.
Casey drew this triangle on the coordinate
plane.
NAME ______________________________________________ DATE
9-1
____________ PERIOD _____
Enrichment
Reflections in the Coordinate Plane
Study the diagram at the right. It shows how the
triangle ABC is mapped onto triangle XYZ by the
transformation (x, y) → (⫺x ⫹ 6, y). Notice that 䉭XYZ
is the reflection image with respect to the vertical
line with equation x ⫽ 3.
(x, y) → (⫺x ⫹ 6, y)
y
Y
B
1. Prove that the vertical line with equation x ⫽ 3 is the
perpendicular bisector of the segment with endpoints
(x, y) and (⫺x ⫹ 6, y). (Hint: Use the midpoint formula.)
X
O
x
Z
C
x⫽3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Every transformation of the form (x, y) → (⫺x ⫹ 2h, y) is
a reflection with respect to the vertical line with equation
x ⫽ h. What kind of transformation is (x, y) → ( x, ⫺y ⫹ 2 k)?
Draw the transformation image for each figure and the given
transformation. Is it a reflection transformation? If so, with
respect to what line?
3. (x, y) → (⫺x ⫺ 4, y)
4. (x, y) → (x, ⫺y ⫹ 8)
y
O
Chapter 9
y
O
x
11
x
Glencoe Geometry
Lesson 9-1
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