Name
Class
Date
Enrichment 12-1
Lines of Reflection
A line of reflection is the line in which the preimage is reflected to create
the image. When a reflection is shown on a grid, you can use algebra to
locate and give the equation of the line of reflection.
6
Use the figure at the right to complete Exercises 1–6.
y
L
K
4
1. What point is halfway between J and J⬘?
2
L'
J
2. What point is halfway between K and K⬘?
0
ⴚ6 ⴚ4 ⴚ2
3. What point is halfway between L and L⬘?
J'
4. What formula did you use in Exercises 1–3?
5. Use the points found in Exercises 1–3 to draw the line of reflection.
4
6 x
ⴚ2
ⴚ4
A
2
K'
ⴚ6
6. What is the equation of the line of reflection?
Draw the line of reflection on each grid. Then give the equation of the line of reflection.
7.
y
4
T'
8.
D
4
S'
E'
2
6x
F'
0
ⴚ6 ⴚ4
R'
R
ⴚ4
ⴚ6
Q
y
D'
2
ⴚ2 0
ⴚ2
ⴚ6
Q'
6
6x
4
F
ⴚ4
E
S
ⴚ8
2
ⴚ6
© Pearson Education, Inc. All rights reserved.
T
9.
y
6
A
10.
M
4
2
ⴚ6 ⴚ4
0
B
ⴚ2
D'
C
ⴚ4
2
B'
6 x
12.
W'
ⴚ4
ⴚ6
G'
4
6x
2 J' 4
6x
Q
y
U
4
2
T'
ⴚ8 ⴚ6 ⴚ4 ⴚ2 0
ⴚ2
P
0
N' ⴚ6 ⴚ4 ⴚ2
ⴚ2
Q'
ⴚ4
P'
ⴚ6
C'
U'6 y
V'
N
2
ⴚ6
11.
y
M'
A'
D
6
4
V
6x
T
W
H'
I'
K'
ⴚ8 ⴚ6 ⴚ4 ⴚ2 0
H ⴚ2
G
I
ⴚ6
J
K
Geometry Chapter 12
Lesson 12-1 Enrichment
15
Chapter 12 Answers
(continued)
5.
5.
6
line symmetry in the dashed
lines, rotational symmetry
around points, translational
symmetry, glide reflectional
symmetry
y
L
K
4
2
L'
J
0
ⴚ6 ⴚ4 ⴚ2
Reteaching 12-7
6 x
4
ⴚ2
J'
1. Check students’ work.
y
2.
2
ⴚ4
4
K'
ⴚ6
2
2
ⴚ4
4
ⴚ6 ⴚ4 ⴚ2
Q'
4
2
ⴚ4
O
ⴚ2
2
y = -4
8.
4
6
2
D'
2
4
6
8
12
10
2
ⴚ6 ⴚ4 ⴚ2
y
0
2
6x
4
ⴚ2
F
ⴚ4
E
ⴚ6
y = -x
9.
6
A
2 4 6 8 x
D
0
B
ⴚ2
ⴚ12
C
ⴚ4
4. the midpoint formula: M =
Answers
A'
D'
2
ⴚ6 ⴚ4
2. (-1, 0)
y
4
ⴚ4
ⴚ6
ⴚ8
ⴚ10
2
B'
x
6
C'
ⴚ6
Enrichment 12-1
40
E'
F'
6
4
2
ⴚ2
y
4
D
12 x
ⴚ4
1. (-3, -1)
S
T
y
ⴚ8 ⴚ6
R'
R
ⴚ8
ⴚ8 ⴚ6 ⴚ4 ⴚ2 O
ⴚ2
6x
2 S'4
ⴚ6
Q
4.
5.
0
ⴚ2
ⴚ4
4 x
ⴚ4
ⴚ12
y
2
T'
y
3.
1
2
6. y = 12 x +
7.
4 x
x=1
3. (5, 3)
x1 1 x2 y1 1 y2
(
2
,
2
)
Geometry Chapter 12
© Pearson Education, Inc. All rights reserved.
ⴚ4 ⴚ2 O
ⴚ2
Chapter 12 Answers
10.
M
6
(continued)
y
Enrichment 12-4
N
1.–9. Check students’ work.
10. 12-3; rotation; twice
11. 130
12. 100
13. 160
M'
2
P
0
ⴚ8 ⴚ6 ⴚ4 ⴚ2
N'
ⴚ2
Q'
ⴚ4
P'
6x
4
Q
ⴚ6
y = -2x - 2
11.
U'
V'
6
y
U
4
2
W'
T'
ⴚ8 ⴚ6 ⴚ4 ⴚ2
0
V
6x
4
ⴚ2
T
Enrichment 12-5
1. yes; rotational and point symmetry
2. no
3. yes;
rotational and point symmetry
4. yes; rotational and point
symmetry
5. no
6. no
7. diamonds
8. 12
9. Seven of diamonds; this does not have symmetry because
the diamond in the middle is toward either the bottom or top
of the card, and when you rotate the card 180°, the position
will be reversed.
10. All the face cards have symmetry.
11. yes; 2, 4, 10
12. No; Sample: When you look at the
card one way, three of the points of the hearts are pointing
down, and five are pointing up. When you rotate the card 180º,
five of the points of the hearts are pointing down, and three
are pointing up.
13. No; because the number and suit of
each card are placed in opposite corners, none of the cards
have line symmetry.
14. You can add a backward 3 with
the small club below it to the two empty corners to create line
symmetry, or you can remove the 3 with the small club below
it from each of the two corners.
W
ⴚ4
Enrichment 12-6
ⴚ6
y = 3x + 2
12.
y
G'
6
© Pearson Education, Inc. All rights reserved.
4
H' 2
I'
ⴚ8 ⴚ6 ⴚ4 ⴚ2
H ⴚ2
0
G
I
ⴚ4
2 J' 4
K'
6x
J
ⴚ6
K
y = -12 x - 1
Enrichment 12-2
1. -7, -2
2. 4, -7
3. -10, 5
4. -3, -9
5. Foster
6. yes
7. Wilson
8. -7, -3
9. C
Enrichment 12-3
1. (0, -2, 3)
2. (-2, -2, 3)
3. (-2, -2, 0)
4. (0, -2, 0)
5. (0, -6, 0)
6. (0, -6, 3)
7. (-2, -6, 3)
8. (-2, -6, 0)
9. (2, 0, 3)
10. (2, -2, 3)
11. (2, -2, 0)
12. (2, 0, 0)
13. (6, 0, 0)
14. (6, 0, 3)
15. (6, -2, 3)
16. (6, -2, 0)
Enrichment 12-7
1a. (2, 0, 2)
1e. (2, 0, 0)
2a. (4, 0, 4)
2e. (4, 0, 0)
3. (0, 0, 0)
1b. (0, 0, 2)
1c. (0, 2, 2)
1d. (2, 2, 2)
1f. (0, 0, 0)
1g. (0, 2, 0)
1h. (2, 2, 0)
2b. (0, 0, 4)
2c. (0, 4, 4)
2d. (4, 4, 4)
2f. (0, 0, 0)
2g. (0, 4, 0)
2h. (4, 4, 0)
4. 2
5. Each edge in the image is double
that in the preimage.
6. Samples: Three faces are
coplanar for image and preimage; three faces are parallel;
Geometry Chapter 12
Answers
41