Square
Rectangle
Rhombus
Parallelogram
Trapezoid
Isosceles Triangle
Equilateral Triangle
Isosceles Trapezoid
Regular Pentagon
Regular Hexagon
Regular n-sided Polygon
2. Transformation / Rule / Rigid Motion
(Yes or No) / Direct Isometry
(Yes or No) / Indirect Isometry (Yes or No)
Reflection over the x-axis
Reflection over the y-axis
Reflection over y =x
Reflection over y = -x
Translationa, b
Dilation of K units
Rotation of 90°
Rotation of 180°
Rotation of 270°
Rotation of -90°
Rotation of -180°
Rotation of -270°
Point Reflection through the origin
3. Which letters have Point Symmetry?
4. Which letters have point symmetry, but do not have lines of symmetry?
5. Write a rule for the following transformations:
a) R90° ◦ D3 ◦ x-axis (x, y)
b) D3 ◦ R90° ◦ D-2 ◦ T4, -2 (x, y)
c) ry=-x ◦ R270° ◦ T1, 0 ◦ Rorigin (x, y)
6. If point A(4, 2) is reflected over line m where the image point is A’(1, 9), find the equation of line m.
7. Perform the following transformation
R(1, 3) (4, 7) / 8. Perform the following transformation
R(-2, 5) (6, 9)
9. Perform the following transformation
R(4, 0) (1, 8) / 10. Perform the following transformation
R(0, 5) (-2, 9)
11. Perform the following transformation
D2, (1, 4) (3, 6) / 12. Perform the following transformation
D3, (-2, 7) (3, 2)
13. Using the Regular Octagon below, answer the following questions.
a) R90° ◦ rl (B) / b) R135° ◦ rl ◦ rm (D) / c) R-270° ◦ rl ◦ R135° (F)d) rm ◦ R-225° ◦ rl (C) / e) rm ◦ rl ◦ rm ◦ rl (E) / f) R45° ◦ R180° ◦ rm (D)
14. D-3,p (A) = A’
A
P
15. Name all transformations that preserve orientation.
16. A double line reflection over parallel lines is equivalent to what transformation
17. A double line reflection over intersecting lines is equivalent to what transformation
18. A line reflection followed by a translation in the direction of the line reflection is equivalent to what transformation?
19. Explain the difference between a Direct Rigid Motion versus an Indirect Rigid Motion.
Part II.
Match the following letters with the correct transformation rule.
1. (x, y) → (x, -y)2. (x, y) → (-x, y)
3. (x, y) → (y, x)
4. (x, y) → (x + 2, y + 3)
5. (x, y) → (3x, 3y)
6. (x, y) → (-x, -y)
7. (x, y) → (-y, x) / a. Point reflection through the origin
b. Point reflection through point (4, 1)
c. Reflection over the x-axis
d. Reflection over the y-axis
e. Reflection over the line y = x
f. Reflection over the line y = -x
g. Reflection over the line x = 2
h.
i.
j.
k.
l.
m.
n.
o.
p.
1. Given an example of a transformation that is not a Rigid Motion that preserves orientation:
2. Given an example of a letter that has point symmetry and two lines of symmetry:
3. Given an example of a letter that has point symmetry and no lines of symmetry:
4. Which of the following transformation is a direct isometry?
a) (x, y) → (y, x) b) (x, y) → (x, -y) c) (x, y) → (-x, -y) d)
5. Which transformation is not a Rigid Motion?
a) b) c) d)
6. The image of a point after a dilation of 4 is (4, 2). Find the original point.
a) (1, ½) b) (16, 8) c) (8, 6) d) (0, -2)
1. / Which letter has point symmetry?(1) A (3) H
(2) B (4) W
2. / Which shape does not have rotational symmetry?
(1) trapezoid (3) circle
(2) regular pentagon (4) square
3. / Which letter has both point and line symmetry?
(1) Z (3) C
(2) T (4) H
4. / Which letter has point symmetry but not line symmetry?
(1) H (3) T
(2) S (4) X
5. / Which letter below has point symmetry, but does not have line symmetry?
(1) H (3) A
(2) N (4) E
6. / Helen is using a capital H in an art design. The H has
(1) only one line of symmetry
(2) only two points of symmetry
(3) two lines of symmetry and only one point of symmetry
(4) two lines of symmetry and two points of symmetry
7. / Triangle A’B’C’ is the image of ∆ABC under a dilation such that A’B’ = 3AB. Triangles ABC and A’B’C’ are
(1) congruent but not similar
(2) similar but not congruent
(3) both congruent and similar
(4) neither congruent nor similar
8. / Under the transformation which property is not preserved?
(1) distance (3) parallelism
(2) orientation (4) angle measure
9. / What is the image of (x,y) after a translation of 3 units right and 7 units down?
(1) (x + 3,y – 7) 3) (x – 3,y – 7)
(2) (x + 3,y + 7) (4) (x – 3,y + 7)
10. / What is the image of point (–3,–1) under a reflection in the origin?
(1) (3,1) (3) (1,3)
(2) (–3,1) (4) (–1,–3)
11. / Point (-2, 3) is reflected in the x-axis. In which quadrant does its image lie?
(1) I (3) III
(2) II (4) IV
12. / Which image represents a line reflection?
Part III: Constructing Transformation:
1. /2. /
3. /
4. /
5. /
6. /
7. /
8. /
9. /
10. /