A  rotation is equivalent to  of a complete rotation, so rotate as follows:

The image of  under this rotation, which we will call , is at .

Now, construct , and reflect the hexagon about this line:

The image of  under this reflection - the desired  - is located at  itself.

Between 6:15 and 6:40,

minutes elapse.

The minute hand of a clock rotates one complete clockwise turn about its mount over the course of 60 minutes. Therefore, over 25 minutes, the minute hand rotates clockwise.

The hour hand of a clock makes one complete  clockwise rotation over the course of 12 hours, or

minutes.

Therefore, over the course of 20 minutes, the hour hand rotates

.

The minute hand of a clock rotates one complete clockwise turn about its mount over the course of 60 minutes, or, equivalently, since there are 60 seconds in a minute, every

seconds.

Over the course of 1 minute 40 seconds - or, since one minute is equal to 60 seconds,  seconds - the minute hand rotates clockwise

.

Examine the figure below:

If we connect the horizontal line with the line along the rotated nine at right, we see that it is the result of a one-third turn clockwise; the angle between them 

Examine the figure below:

If we connect the horizontal line with the line along the rotated nine at right, we see that it is the result of a one-eighth turn clockwise; the angle between them .

Examine the figure below. 

If we connect the horizontal line with the line along the rotated "omega" at right, we see that it is the result of a one-sixth turn counterclockwise; the angle between them is one sixth of , or  .

The hour hand of a clock makes one complete  clockwise rotation over the course of 12 hours, or, since one hour is equal to 60 minutes,

Therefore, over the course of 1 hour 20 minutes - which is equal to minutes - the hour hand rotates

.

The circumcenter of a triangle can be located by finding the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisectors are shown below, with point of intersection  :

It can be seen that, as is characteristic of a right triangle, this point is the midpoint of the hypotenuse. Construct . A dilation of scale factor   with center  can be performed by letting , , and  be the midpoints of , , and , respectively: 

Removing the perpendicular bisectors and , we see that the correct choice is the figure

The centroid of a triangle can be located by finding the intersection of the three medians of the triangle - the segments that connect each vertex to the midpoint of its opposite side. The medians are shown below, with point of intersection  :

A dilation of scale factor   with center  can be performed by letting , , and  be the midpoints of , , and , respectively: 

Removing the medians and , we see that the correct choice is the figure