The hexagon GIKMPR is regular. The dashed line segments form 30-degree angles. What is the image of ON after a rotation of 180 degrees?
ON
OH
OJ
OL
The image of ON after a rotation of 180 degrees is OL.
To find the image of ON after a rotation of 180 degrees, we need to imagine rotating the hexagon GIKMPR by 180 degrees, keeping the center of rotation at the origin.
A rotation of 180 degrees means that each point is rotated halfway around the center point. So, to find the image of ON, we draw a line connecting the origin (O) to the point N. Then, we rotate this line by 180 degrees.
Since the hexagon is regular, meaning that all sides and angles are equal, we can use symmetry to determine the point opposite to N on the hexagon. In a regular hexagon, each side is parallel to the side opposite to it.
Therefore, the image of ON after a rotation of 180 degrees is the point opposite to N on the hexagon. In this case, the point opposite to N is the point L.
So, the answer is OL.
To find the image of point O after a rotation of 180 degrees in a regular hexagon, we need to understand the properties of a regular hexagon and the effect of a 180-degree rotation.
A regular hexagon is a polygon with six equal sides and six equal interior angles, each measuring 120 degrees. The properties of a regular hexagon ensure that if we rotate it by multiples of 60 degrees, the hexagon will coincide with its original position.
In a regular hexagon, the dashed line segments forming 30-degree angles imply that each line segment connects the center of the hexagon to a vertex, dividing the hexagon into twelve 30-60-90-degree triangles.
Now, let's use this information to determine the image of point O after a 180-degree rotation. Since the rotation is 180 degrees, it will bring point O to the opposite side of the hexagon.
Start by drawing a diagram of the regular hexagon, labeling the vertices G, I, K, M, P, and R. Then, label point O, which is the center of the hexagon. Next, draw a dashed line segment connecting O to point N.
To find the image of point O after the 180-degree rotation, draw a line passing through point O and parallel to line segment GIKMPR. This line will intersect the opposite side of the hexagon, parallel to the line segment GIKMPR.
Label the intersection point of the parallel line and the opposite side of the hexagon as O'. This point represents the image of point O after a 180-degree rotation.
Finally, determine which of the given options (ON, OH, OJ, OL) corresponds to the image point O'.
To summarize, the image of point O after a 180-degree rotation will be represented by the option that corresponds to the intersection point O' obtained by drawing a line through point O, parallel to line segment GIKMPR, and intersecting the opposite side of the hexagon.
Please note that without a provided diagram or additional context, it is not possible to determine the specific option corresponding to the image point O'.