A square rotated about its center by 360º maps onto itself at: a) 1 B) 2 C) 3 D) 4 different angles of rotation. You can reflect a square onto itself across A) 2 B) 4 C) 8 D) 16 different lines of reflection.

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26-03-2017
Mathematics

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A square rotated about its center by 360º maps onto itself at: a) 1 B) 2 C) 3 D) 4 different angles of rotation. You can reflect a square onto itself across A) 2 B) 4 C) 8 D) 16 different lines of reflection.

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JeanaShupp JeanaShupp · Answer 1 · 2019-03-08T09:10:50+01:00

Answer: A square rotated about its center by 360º maps onto itself at D) 4 different angles of rotation. You can reflect a square onto itself across B) 4 different lines of reflection.

Step-by-step explanation:

A square is a geometric figure which has all its four sides equal and all its interior angles are right angles( [tex]90^{\circ}[/tex]) .

Therefore, it can be rotated about its center by [tex]360^{\circ}[/tex] .

It maps onto itself at 4 different angles of rotation ( at every [tex]90^{\circ} angle[/tex]).

We can reflect a square onto itself across 4 different lines of reflection (2 across the non-parallel sides and 2 across the vertices of the square).

MrRoyal MrRoyal · Answer 2 · 2022-02-14T14:35:37+01:00

The true statements are:

A square rotated about its center by 360º maps onto itself at 4 different angles of rotation.
You can reflect a square onto itself across 4 different lines of reflection.

The angles in a square are 90 degrees.

So, the number of times the square maps onto itself when rotated is:

[tex]n = \frac{360}{90}[/tex]

Evaluate the quotient

[tex]n = 4[/tex]

Hence, the solution to both statements is 4