Question

1.)A pentagon is translated down and to the left. How many sides does the resulting figure have?

a)6
b)5
c)4
d)It is impossible to determine without knowing how far the pentagon was translated.

3.)Which of the following capital letters results in the same letter over again when reflected about a horizontal line?
a)D
b)S
c)Y
d)A

4.) A quadrilateral has vertices A, B, C, and D. A line of reflection is drawn so that A is 6 units away from the line, B is 4 units away from the line, C is 7 units away from the line, and D is 9 units away from the line. When quadrilateral ABCD is reflected about the line of reflection to create a new quadrilateral A′B′C′D′, which resulting point is closest to the line of reflection?

a)D′
b)B′
c)A′
d)C′

5.) A pre-image arrow pointing east is rotated 135° clockwise. In which direction is the image arrow pointing?

a)southwest
b)west
c)northwest
d)southeast

6.) A point is rotated 272° clockwise. What is the equivalent smallest positive counterclockwise rotation?

written answer

9.)A rotation by how many degrees represents six full rotations?

written answer

10.)What is true about the number of sides in any regular polygon that has at least one line of symmetry passing through two vertices?

a)The number of sides is prime.
b)The number of sides is odd.
c)The number of sides is a perfect square.
d)The number of sides is even.
14.)
15.)Which of the following series of transformations is equivalent to reflecting about the line y=−x?

a)reflecting about the y-axis and then rotating 90° counterclockwise
b)reflecting about the x-axis and then rotating 180° counterclockwise
c)reflecting about the y-axis and then rotating 180° counterclockwise
d)reflecting about the x-axis and then rotating 90° counterclockwise

16.)Which point maps to itself both when reflected about y=x and reflected about y=−x?

a)(−1,1)
b)(0,0)
c)(1,1)
d)(0,1)

17.)True or false: Sequences of rigid motions can be applied to any type of polygon.

a)This statement is false. Sequences of rigid motions can only be applied to polygons with fewer than 10 vertices.
b)This statement is false. Sequences of rigid motions can only be applied to convex polygons.
c)This statement is true.
d)This statement is false. No more than one rigid motion can be applied to any polygon.

18.) True or false: A sequence of rigid motions that maps a pre-image to an image must contain no fewer than two unique rigid motions for the pre-image and the image to be congruent.

a) This statement is false. If a sequence of rigid motions maps a pre-image to an image, the pre-image and the image are congruent no matter the details of the sequence of rigid motions.
b)This statement is true.
c) This statement is false. A sequence of rigid motions that maps a pre-image to an image must contain no more than two unique rigid motions for the pre-image and the image to be congruent.
d) This statement is false. A sequence of rigid motions that maps a pre-image to an image must contain exactly two unique rigid motions for the pre-image and the image to be congruent.

Answer 1

1) b) 5

3) a) D

4) b) B'

5.) a)

6.) 88°

9) 2,160°

10.) d) The number of sides is even

15.) a) Reflecting about the y-axis and then rotating 90° counterclockwise

16) b) (0, 0)

17.) c) This statement is true

18.) a) This statement is false. If a sequence of rigid motions maps a pre-image to an image, the pre-image and the image are congruent no matter the details of the sequence of rigid motions

Explanation:

1) b) 5 A translation is a form of rigid transformation that preserves the shape and dimensions of the pre-image in the image

3) a) D. The letter D has an horizontal line of symmetry

4) b) B'. The reflection of an object about a line is as far behind the mirror as the object is in front

5.) a) The arrow will point in the southwest direction

6.) 88°. A 272° rotation clockwise, is equivalent to a 360° - 272° rotation. anticlockwise

9) 2,160°.

One rotation = 360°, 6 rotations = 6 × 360° = 2,160°

10.) d) The number of sides is even

The existence of a line symmetry gives equal number of sides on both sided of the line of symmetry, which gives an even an even number of sides

15.) a) Reflecting about the y-axis and then rotating 90° counterclockwise

Reflecting across the line y = -x, gives (x, y) → (-y, -x)

Reflecting about the y axis gives, (x, y) → (x, -y))

Rotation 90° counterclockwise gives (x, -y) → (-y, -x)

16) b) (0, 0),

Reflection about the line y = x gives (x, y) → (y, x)

Reflection about the line y = -x gives (x, y) → (-y, -x)

When, (x, y) = (0, 0), (y, x) ≡ (-y, -x)

when

17.) c) This statement is true,

A rigid motion involves the equal change of all coordinates on the pre-image to form the image

18.) a) This statement is false. If a sequence of rigid motions maps a pre-image to an image, the pre-image and the image are congruent no matter the details of the sequence of rigid motions

The preimage and the image formed by a rigid transformation are always congruent