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 would be OL.
To find the image of point ON after a rotation of 180 degrees, we need to rotate it by an angle of 180 degrees counterclockwise about the center of the regular hexagon GIKMPR.
Since a regular hexagon has six equal sides, the center is the point of intersection of the diagonals. Let's label this point as C.
Since GIKMPR is a regular hexagon, the dashed line segments that form 30-degree angles are the diagonals connecting the non-adjacent vertices.
To rotate a point 180 degrees counterclockwise about the center C, the image of any point will be the point that is the same distance from C, but on the opposite side of the line connecting C and the original point.
Let's label the intersection point of the line segment ON and the line segment connecting points G and M as D.
Now, to find the image of point ON, we can draw a line segment connecting C and D. This line will pass through the center of the hexagon.
Finally, we draw a line segment on the opposite side of CD, starting from C and extending the same distance as the original point ON. The point where this line segment intersects the dashed line segment is the image of point ON after a rotation of 180 degrees.
So, based on the given options, the image of point ON after a rotation of 180 degrees is OL.
To find the image of point O after a rotation of 180 degrees, we need to determine the position of point O after rotating the hexagon 180 degrees counterclockwise around its center.
Since the hexagon GIKMPR is regular, it means that all of its sides are equal in length, and all interior angles are equal. A regular hexagon has internal angles of 120 degrees, so the angle formed by the dashed line segments would be half of that, which is 60 degrees.
First, let's identify the position of point O in relation to the hexagon. Based on the given information, we can assume point O is at the center of the hexagon.
Now, to perform a rotation of 180 degrees, imagine rotating the hexagon GIKMPR counterclockwise around its center by 180 degrees. The rotation will result in the new positions of the other vertices.
The new positions of the vertices will be symmetric to their original positions with respect to the center point O. Since point O is at the center, it will remain unchanged after the rotation. Therefore, the image of point O will be the same as its original position.
So, the image of point ON after a rotation of 180 degrees will be at the same location as the original point ON, which is ON itself.
To summarize, the image of point ON after a rotation of 180 degrees is ON.