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# The order of rotation of a line segment is A.$4$B.$3$C.$1$D.$2$

Last updated date: 22nd Jul 2024
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Hint: First we have to know the order of rotation is the number of times the figure coincides with itself as it rotates through ${360^o}$. We have to know the angle of rotation of a line segment. Then using the definition of order of rotation find the order of rotation of a line segment.

Complete step by step solution:
Rotation is the process or act of turning or circling around something. An example of rotation is the earth's orbit around the sun.
One rotation around a circle is equal to ${360^o}$. An angle measured in degrees should always include the degree symbol $^o$ or the word "degrees" after the number. For example, ${180^o} = 180$ degrees. A complete rotation about the centre point is equal to ${360^o}$ or $2\pi$ radians. The rule for a rotation by ${180^o}$ about the origin is $\left( {x,y} \right) \to \left( { - x, - y} \right)$ .
In geometry, a line segment is a part of a line that is bounded by two distinct endpoints, and contains every point on the line that is between its endpoints.
The angle of rotational symmetry or angle of rotation is the smallest angle for which the figure can be rotated to coincide with itself. Example: The angle of rotation is ${60^o}$ and the order of the rotational symmetry is $6$.
The angle of rotation of a line segment is ${180^o}$.
So, order of rotation of a line segment is $\dfrac{{{{360}^o}}}{{{{180}^o}}} = 2$.
Hence, the Option (D) is correct.
So, the correct answer is “Option D”.

Note: Note that the order of rotational symmetry of a circle is how many times a circle fits onto itself during a full rotation of $360$ degrees. A circle has an infinite 'order of rotational symmetry'. In simplistic terms, a circle will always fit into its original outline, regardless of how many times it is rotated.