Question

If the figure below is rotated a certain number of degrees, the transformed figure will coincide with (overlap) the original. Which of these rotations will not result in the transformed figure coinciding with the original?

a) 90 degrees
b) 180 degrees
c) 270 degrees
d) 360 degrees

Answer 1

All listed rotations (90, 180, 270, and 360 degrees) could result in a figure coinciding with its original position depending on the symmetry of the figure. Without the specific image of the figure, determining which rotation will not result in coincidence is impossible, but a 360-degree rotation guarantees that the figure will coincide with itself for any figure.

Step-by-step explanation:

The question asks which rotation of a geometric figure will not result in the transformed figure coinciding with the original figure. This involves understanding properties of geometric transformations, particularly rotations. When a figure is rotated by multiples of 360 degrees, it will always coincide with its original position. Therefore, rotations of 90, 180, 270, and 360 degrees will result in the figure overlapping itself if the figure is symmetric with respect to these rotation angles.

For the given options:

• 90 degrees - For a square or a circle, it would coincide after this rotation.
• 180 degrees - Any figure with bilateral symmetry would overlap after this rotation.
• 270 degrees (which is equivalent to a -90 degrees rotation) - Similar to a 90 degrees rotation, symmetric figures like a square or a circle would coincide.
• 360 degrees - This is a full rotation, and any figure will overlap with itself after rotating a full cycle.

Therefore, all listed rotations could potentially result in a figure that coincides with its original position. Without the image of the figure, it's not possible to definitively determine which rotation will not result in coincidence, but generally speaking, 360 degrees is a rotation that should always result in the figure coinciding with itself.

Answer 2

For a figure with 6 flower petals, rotations of 90 and 270 degrees will not result in the figure coinciding with its original position as they are not divisible by the rotational symmetry of 60 degrees (Options A and C).

Step-by-step explanation:

If we consider a figure with a 6 flower petals design, when this figure is rotated around its center, it will coincide with its original position if the rotation angle is a divisor of 360 degrees since there are 360 degrees in a full rotation.

However, considering the particular geometry of a figure with 6 petals, it will coincide with its original position every 60 degrees of rotation because the figure has rotational symmetry. This is because 360 degrees divided by the number of petals (6) gives us the degrees needed for one full symmetry rotation, which is 60 degrees.

Let's look at the options provided:

• 90 degrees - A rotation of 90 degrees will not result in the 6-petal figure coinciding with its original position because 90 is not divisible by the rotational symmetry of 60 degrees.
• 180 degrees - A rotation of 180 degrees is 3 times 60, so the 6-petal figure will coincide with its original position.
• 270 degrees - A rotation of 270 degrees is also not divisible by 60 and will not result in the original overlap.
• 360 degrees - A full rotation of 360 degrees will always result in the original overlap for any figure.

Therefore, the rotations that will result in the transformed figure coinciding with the original are 180 degrees and 360 degrees. The rotations of 90 degrees and 270 degrees will not result in an overlap of the figure with 6 flower petals, which corresponds to Options A and C.

Your question is incomplete, but most probably your full question can be seen in the attachment.