7. This snowflake has rotational symmetry. Trace the snowflake. Rotate the tracing clockwise about the centre. How many turns produce an exact copy of the original snowflake before you get back to where you started?
The image of the snowflake is not provided, so it is not possible to determine the number of turns that produce an exact copy of the original snowflake before getting back to where you started.
To determine how many turns produce an exact copy of the original snowflake before getting back to where you started, we need to figure out the rotational symmetry of the snowflake.
1. Start by tracing the snowflake on a piece of paper.
2. Place a point in the center of the snowflake, marking it as the rotation point.
3. Rotate the tracing clockwise by 60 degrees (1/6 of a full rotation) around the center.
4. Check if the rotated tracing matches the original snowflake. If it does, note that you have completed 1 full turn.
5. Continue rotating the tracing clockwise by another 60 degrees and check for a match.
6. Repeat step 5 until you get back to where you started.
The number of turns it takes to get back to the initial position is the number of matching rotations.
Since the snowflake has rotational symmetry, it has six identical arms. Thus, each 60-degree rotation will create an exact copy of the original snowflake. After rotating the tracing six times by 60 degrees, you will get back to where you started.
Therefore, it takes 6 turns to produce an exact copy of the original snowflake before returning to the initial position.