Question

The figure has 45° rotational symmetry. Which rotation about point P maps B onto D? Options: Option 1: A 45° counterclockwise rotation Option 2: A 90° counterclockwise rotation Option 3: A 180° counterclockwise rotation Option 4: A 270° counterclockwise rotation

Answer 1

The correct answer is Option 2.) The rotation about point P that maps B onto D, for a figure with 45° rotational symmetry, is a 90° counterclockwise rotation.

Step-by-step explanation:

The student has asked about the rotation around point P that maps point B onto point D, given a figure with 45° rotational symmetry. To determine which rotation maps B onto D, one must consider the rotational symmetry and the positions of the points. If the figure has a symmetry of 45°, this means that each rotation by 45° will map every point to another point in the same relative position.

Option 2: A 90° counterclockwise rotation would be the correct choice. This is because two steps of 45° rotational symmetry are required to map B onto D, which adds up to a total of 90 degrees.

Answer 2

A 270° counterclockwise rotation maps B onto D.

Therefore, correct answer is Option 4: A 270° counterclockwise rotation maps B onto D.

Step-by-step explanation:

Rotational symmetry refers to the ability of a shape to look the same after some rotation. In this case, the figure has 45° rotational symmetry, meaning it looks the same after a 45° rotation. To map point B onto D, we need a 270° rotation because 270° is a multiple of 45° and brings B to the same position as D. Options 1, 2, and 3 do not achieve this alignment; only a 270° counterclockwise rotation corresponds to the 45° rotational symmetry.

Rotational symmetry in geometry and its applications in understanding the repetitive patterns and shapes that retain their appearance after a certain rotation. Recognizing rotational symmetry is essential in various fields, including art and design.

Therefore, correct answer is Option 4: A 270° counterclockwise rotation maps B onto D.