Lines of Symmetry, Diagonals, Rotation

The figure below shows two perpendicular lines 𝑗 and 𝑘 intersecting at point 𝐷 in the interior of a rectangle. Line 𝑗 bisects both the top and bottom sides of the rectangle. Line 𝑘 bisects both the left and right sides of the rectangle. Which transformation will always carry the figure onto itself?

Select All that apply.

• a reflection across line 𝑗.

• A reflection across line 𝑘.

• A rotation of 90° clockwise about point 𝐷.

• A rotation of 180° clockwise about point 𝐷.

• A rotation of 270° clockwise about point 𝐷.

Describe the rotational symmetry for a regular pentagon.

• A regular pentagon has a central angle of 72° and will map onto itself after rotations of 72°, 144°, 216°, and 288°.

• A regular pentagon has five axes of symmetry.

• A regular pentagon has four-fold rotational symmetry.

• A regular pentagon has a central angle of 45° and will map onto itself after rotations of 45°, 90°, 135°, 180°, 225°, 270°, and 325°.

Which transformation carries the parallelogram below onto itself?

• a reflection over y = x

• a reflection over y = −x

• a rotation of 90° counterclockwise about the origin

• a rotation of 180° counterclockwise about the origin

Which transformation will map the rectangle onto itself?

• 90 degree rotation about the center point

• 180 degree rotation about the center point

• reflection across the x axis

• reflection across the bue line

Which line of reflection will NOT carry the square onto itself?

• y = 0

• x = 0

• y = x

• x = 5

Which of the following transformations carry this regular polygon onto itself?

• Rotation of 144 degrees counterclockwise

• Rotation of 120 degrees counterclockwise

• Rotation of 90 degrees counterclockwise

• Rotation of 64 degrees counterclockwise

Which transformation would not carry a square onto itself?

• a reflection over one of its diagonals

• a 90° rotation clockwise about its center

• a 180° rotation about one of its vertices

• a reflection over the perpendicular bisector of one side

Choose ALL the degrees of rotation that will map a regular hexagon onto itself.

• 90

• 120

• 150

• 240

• 300

A reflection across which line will carry the figure onto itself?

• x = -2

• y = x

• y = -2

• x = -1

Which of the following transformation will map the trapezoid onto itself?

• reflection across the blue line

• 90 degree rotation about the center point

• 180 degree rotation about the center point

• 270 degree rotation about the center point