How do you write Rotation, Translation, and Rotational Symmetry in math. For example, reflection is written : a reflection in line l is indicated by ML.
Rotation: In math, a rotation is described by the letter "R" followed by the angle of rotation and the center of rotation. For example, a rotation of 90 degrees clockwise about the origin would be represented as R90.
Translation: A translation is indicated by the letter "T" followed by the vector representing the amount and direction of the translation. The vector can be written in terms of the horizontal and vertical shifts. For example, a translation of 3 units to the right and 2 units up would be represented as T(3, 2).
Rotational Symmetry: Rotational symmetry can be represented by the letter "RS" followed by the angle of rotation and the center of rotation, similar to how a rotation is written. For example, an object with rotational symmetry of order 4 (meaning it can be rotated by multiples of 90 degrees and still look the same) about the origin would be represented as RS90.
In mathematics, Rotation, Translation, and Rotational Symmetry can be represented using specific notation. Here's how each of them is typically written:
1. Rotation:
- A rotation is usually denoted by "R" followed by the angle of rotation in degrees.
- The center of rotation is often written as a subscript.
- For example, if you want to express a rotation of 90 degrees counterclockwise (CCW) around the point (2, 3), it can be written as R90(2, 3).
2. Translation:
- A translation is denoted by a lowercase letter "t" followed by a vector that represents the direction and distance of the translation.
- The vector is written within parentheses.
- For example, if you want to indicate a translation 5 units to the right (along the x-axis) and 3 units up (along the y-axis), it can be written as t(5, 3).
3. Rotational Symmetry:
- Rotational symmetry is often represented by the capital letter "C" followed by a number, which indicates the order of rotational symmetry.
- The axis of rotation is usually written as a subscript to the "C" symbol.
- For example, if you want to express a shape with rotational symmetry of order 4 around the origin, it can be written as C4(0).
Note: Different notations may be used depending on the specific mathematical context or textbook being used.