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Math Activity 11.2
11.27
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MATH ACTIVITY 11.2
Rotating, Reflecting, and Translating Figures on Grids
Materials: Tracing paper (suggested) or Pattern Block Virtual Manipulatives.
Virtual
Manipulatives
*1. The shaded triangle shown below on the left can be turned (rotated) about either point
F or point G so that it coincides with (fits exactly on top of) triangle 5. It can also be
rotated about the lettered points so that it coincides with all the other numbered triangles except one. Record the letters of the points about which the shaded triangle can be
rotated to coincide with these other triangles.
Triangle
1
2
3
4
Center of rotation
www.mhhe.com/bennett-nelson
5
6
7
8
9
10
11
F, G
↔
H
A
M
F
1
3
2
5
G
B
7
6
S
Triangle
4
E
Line of reflection
9
8
1
2
3
4
5
6
7
8
9
10
11
↔
AG
10
R
N
C
2. The shaded triangle at the left can be flipped (reflected) about line AG (think of extending AG) to coincide with triangle 1. Find the seven other triangles to which the
shaded triangle can be reflected. Record each triangle that the shaded triangle can be
reflected onto, and the line about which it is reflected.
D
11
3. The shaded triangle at the left can be slid without any turning motion (translated) to
coincide
with triangle 2. This can be visualized
by imagining point H sliding down line
↔
↔
HB to point A, point F sliding down line FG to coincide with point G, and point A slid↔
ing down line AB to point B. Find the four other triangles that the shaded triangle can
be translated onto.
*4. In activity 1, the shaded triangle could not be rotated onto triangle 8. However,
it can
↔
be rotated about point G onto triangle 11 and then reflected about line CD to coincide
with triangle 8. Find three other triangles that the shaded triangle can be rotated to and
then reflected onto triangle 8.
A
B
1
E
4
K
8
Q
2
F
5
J
3
6
H
7
N
10
S
D
G
M
9
R
C
P
11
T
V
5. a. The shaded square shown at the left can be rotated about a lettered point to coincide
with eight of the 11 numbered squares. Find each square to which it can be rotated
and the point about which it is rotated.
b. The shaded square can be reflected onto five of the numbered squares by reflections
about lines through the lettered points. Find each of these squares and the lines
about which the shaded square can be reflected.
c. The shaded square cannot be rotated onto square 2 by a rotation about a lettered
point, but it can be reflected onto square 1 and then rotated onto square 2. Describe
how the shaded square can be reflected and then rotated onto squares 7, 8, 10, and
11. List the lines of reflection and points of rotation.