7.5 – 7.6 in Class assignment key Name: _______________________
Date: _____________
Math 9 **** 7.5 – 7.7 in Class assignment
1. In the figure shown, the order of rotation and Calculate the angle of rotation?
2. Draw a Rotation Image of each of the following shapes.
a) Rotate pentagon ABCDE 90&deg;
b) Rotate parallelogram ABCD 60&deg;
3. How many lines of symmetry does this tessellation have?
4. Which example shows a reflection of triangle X in the dotted line?
Exam ple i
Exam ple ii
X
X
Exam ple iii
Exam ple iv
X
X
5. Draw the reflection image of triangle P using the dotted line as a line of symmetry.
6
y
5
4
3
P
2
1
1
2
3
4
5
x
6. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the
shape by drawing its other half.
y
5
4
3
2
1
1
7. a)
b)
2
3
4
5
6
7
x
Rotate ABC 90&deg; clockwise about vertex C. Draw the rotation image.
Rotate ABC 180&deg; clockwise about vertex C. Draw the rotation image.
A
C
B
8.
Draw the rotation image after a 90&deg; clockwise rotation about vertex A.
P
A
9. a) Reflect shape A in the oblique line through (0, 7) and (7, 0). Label the image shape B.
b) Reflect shape B in the vertical line through 6 on the x-axis. Label the image shape C.
c) Reflect shape C in the oblique line through (5, 0) and (12, 7). Label the image shape D.
y
7
6
5
4
3
A
2
1
1
2
3
4
5
6
7
8
9 10 11 12 13 x
10. This polygon is part of a larger shape. Draw the image of the polygon after each reflection:
i) a reflection in the y-axis
ii) a reflection in the x-axis
iii) a reflection in the oblique line through (–5, 5) and (5, –5)
How many lines of symmetry does the shape have? ______________
y
5
4
3
2
1
–6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
11. a) On the grid below, plot the points A(2, 5), B(2, 6), C(4, 8), D(6, 6), and E(5, 5).
Join the points to form polygon ABCDE.
b) Reflect polygon ABCDE in the oblique line through the points (0, 0) and (8, 8).
Draw the reflection image.
c) Write the coordinates of the larger shape formed by ABCDE and its image.
d) Describe the larger shape and its symmetry.
10
y
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
x
12.
Use the line of symmetry to complete the figure.
13.
a) Reflect the figure over the y-axis. Label the coordinates of the image after the reflection.
b) Is the design now symmetrical?
14. Identify the quadrilaterals that are related to the black quadrilateral by a line of reflection.
9
y
8
7
Q
6
5
R
P
4
3
2
S
1
1
2
3
4
5
6
7
8
9 10 11 12
x
15. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape
by drawing its other half.
y
6
5
4
3
2
1
1
2
3
4
5
6
7
x
16. This polygon is one-half of a shape. Use a vertical line through 5 on the x-axis as a line of symmetry
to complete the shape by drawing its other half. Write the coordinates of the larger shape formed by
PQRS and its image.
y
6
S
5
R
4
3
Q
2
1
P
1
2
3
4
5
6
7
8
9 10
x
A
17. Determine the length of EB in these similar triangles.
5
B
E
7.5
C
20
D
18. Determine the length of QR in this pair of similar triangles
Q
T
6
22.5
P
19. Draw the image of quadrilateral WXYZ after each transformation.
Write the coordinates of each shape formed by quadrilateral WXYZ
and its image. Describe the symmetry in each of these shapes.
a) reflection in the x-axis
b) rotation 90&deg; clockwise about the origin
c) rotation 90&deg; clockwise about the point (1, 0)
d) translation 1 square right and 1 square down
R
9
S