Rotation Reflection and Symmetry

If the given image is rotated 90° counterclockwise, which of the following correctly represents the points A', B', and C' ?

• A'(-4, 4) B'(-1, 2) C'(-3, 0)

• A'(4, -4) B'(1, -2) C'(3, 0)

• A'(4, -4) B'(2, -1) C'(0, -3)

• A'(-4, 4) B'(-2, 1) C'(0, 3)

If the given image is rotated 180°, which of the following correctly represents the points P', Q', R', and S' ?

• P'(-4, 3) Q'(-2, 3) R'(-1, 2) S'(-3, 0)

• P'(3, -4) Q'(3, -2) R'(2, -1) S'(0, -3)

• P'(-3, 4) Q'(-3, 2) R'(-2, 1) S'(0, 3)

• P'(4, -3) Q'(2, -3) R'(1, -2) S'(3, 0)

Which kinds of symmetry does the given shape have (line and/or rotational)? If it has line symmetry, how many lines of symmetry does it have?

• Both Line and Rotational symmetry;

  It has 5 lines of symmetry

• Both Line and Rotational symmetry;

  It has 1 line of symmetry

• Line symmetry only;

  It has 1 line of symmetry

• Rotational symmetry only;

  It has 0 lines of symmetry

Which of the images below can be considered a rotation? (Choose ALL that apply.)

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Given the points A(-2, 3), B(3, 4) and C(0, 1) are rotated 90° clockwise, what is the location of points A', B', and C' ?

• A'(3, 2) B'(4, -3) C'(1, 0)

• A'(-3, 2) B'(-4, -3) C'(-1, 0)

• A'(-3, -2) B'(-4, 3) C'(-1, 0)

• A'(2, -3) B'(-3, -4) C'(0, -1)

Given the parallelogram PQRS with points P(-2, 4), Q(0, 3), R(-2, 2), and S(-4, 3), which graph correctly shows parallelogram P'Q'R'S' after a 180° clockwise rotation?

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Under a rotation about the origin, the point (-3, 4) is mapped to the point (3, -4). What is

the measure of the angle of rotation?

• 90° clockwise

• 180°

• 90° counterclockwise

• none of these are correct.

Triangle ABC is rotated about the origin. The coordinates of point A are (-2, 7) and the coordinates of A' are (-7, -2). Find the angle of rotation.

• 270° clockwise

• 180°

• 270° counterclockwise

• None of these are correct.

How many degrees counterclockwise must car A of the Ferris wheel rotate to get to the original location of car C?

• 60° counterclockwise

• 90° counterclockwise

• 120° counterclockwise

• 135° counterclockwise

How many lines of Symmetry does this hexagon have?

• 3

• 6

• 9

• 12