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 itself

Which statement best describes Lucia's claim?

A. Lucia's claim is correct since any rotation that carries a square onto itself is a multiple of 45°,
B. Lucia's claim is correct since any rotation that is a multiple of 45° carries a square onto itself
C. Lucia's claim is incorrect since not all rotations that carry a square onto itself are multiples of 45,
D. Lucia's claim is incorrect since not all rotations that are multiples of 45° carry a square onto itself

Answer:

The 2 si right

Step-by-step explanation:

We want to study the symmetry of a square and which rotations carry the square into itself.

We will see that the correct option is the last one:

Not all rotations of multiples of 45° carry the square into itself.

Here we have the claim:

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

And we want to see if this is true or not.

What we can try to do, is find a counterexample to see if this is false.

Let's draw a square, then make a point in the center of it, and draw a segment between the center and the right side.

Now rotate that segment around the center of the square (and along with it, the whole square) by 45°.

(note that 45° is a multiple of 45°).

Doing this, you will see that this rotation does not rotate the square into itself.

So the correct option is D, not all rotations of 45° rotate the square into itself. While rotations of 90°, 180°, 270°, etc... will map the square into itself, we just found an example of a rotation of a multiple of 45° that does not do it.

An image of the rotation can be seen below:

If you want to learn more, you can read:

https://brainly.com/question/11392539

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