Lucia draws a square and plots the center of the square. She claims that any rotation about the center of the square that is a multiple of 45" will carry the square onto itselt Which statement best describes Lucia's claim? a. Lucia's claim is incorrect since not all rotations that carry a square onto itself are multiples of 45
b. Lucia's claim is incorrect slace not all rotations that are multiples of 45' carry a square onto itself c. Lucia's daim is correct since any rotation that is a multiple of 45 canles a square onto tselt d. Lucia's calm is correct since any rotation that comes a square onto itself is a multiple of 45

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06-12-2022
Mathematics

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Lucia draws a square and plots the center of the square. She claims that any rotation about the center of the square that is a multiple of 45" will carry the square onto itselt Which statement best describes Lucia's claim? a. Lucia's claim is incorrect since not all rotations that carry a square onto itself are multiples of 45
b. Lucia's claim is incorrect slace not all rotations that are multiples of 45' carry a square onto itself c. Lucia's daim is correct since any rotation that is a multiple of 45 canles a square onto tselt d. Lucia's calm is correct since any rotation that comes a square onto itself is a multiple of 45

Sagot :

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ShubhamSrivastavaidn ShubhamSrivastavaidn · Answer 1 · 2022-12-11T03:12:29-05:00

The statement that best describes Lucia's claim is at option (b), that is " Lucia's claim is incorrect since not all the rotations that are multiples of 45° carry a square onto itself".

What is the rotational symmetry of a square?

Two halves of the square when a mirror line is drawn resemble the same or similar, then that square is said to be in symmetry.
When the square is rotated about an angle, then it remained the same as the original shape, then that square is said to be the rotational symmetry of a square.

Rotation of the given square and its symmetry according to the rotation:

It is given that, Lucia draws a square and plots the center of the square.

Lucia claims that " any rotation about the center of the square that is a multiple of 45° will carry the square onto itself".

To verify this claim, we need to construct a square (ABCD) as shown in the figure.

When the square ABCD is rotated about 45° where we can it is 1 × 45°, the square formed is A'B'C'D' is not the same as the actual one. So, they are not in symmetry after the rotation n this case.

If we rotate again, that is for the second multiple of 45° (2 × 45°), we get a square A''B''C''D''. But, now the square is similar to the actual one. So, they are in symmetry.

This means we can say that, not for all the multiples of 45° rotation, the square does not carry onto itself.

Therefore, we can conclude that "Lucia's claim is incorrect since not all rotations that are multiples of 45' carry a square onto itself".

Learn more about the rotation and symmetry of a square at the following link:

https://brainly.com/question/2333707

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Sagot :

What is the rotational symmetry of a square?

Rotation of the given square and its symmetry according to the rotation:

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