Question

if after a rotation of 45° about a point the figure looks exactly the same then the order of rotation is____?
please find the order of rotation​

Answer 1

If the angle of rotation is 45∘, then symmetry of order is possible and would be 8 rotations

The order of rotational symmetry is that an object has the number of times that it fits on to itself during a full rotation of 360 degrees.

As explained in the definition, we have to check how many times an equilateral triangle fits on to itself during a full rotation of 360 degrees.

Please look at the images of the equilateral triangle in the order A,B and C. A is the original image. The images B and C are generated by rotating the original image A.

When we look at the above images of equilateral triangle, it fits on to itself 3 times during a full rotation of 360 degrees.

So, an equilateral triangle has rotational symmetry of order 3.