The image contains three math problems in Persian about geometric rotation and transformations. Let's solve them step by step:

Problem 7

Question: The first question asks, "To what minimum degree does the shape above need to rotate around point $M$ to map onto itself?"

The shape is symmetric and will map onto itself after rotating 180 degrees.

Answer:
The correct option is $ب$ 180 degrees.

Problem 8

Question: Rotate the given shape 90 degrees clockwise around the red point.

Solution:
When rotating the L-shaped figure 90 degrees clockwise:

• The vertical part of the "L" will shift to the right.
• The horizontal part of the "L" will move down.

If you redraw this shape, the rotated "L" will appear to be oriented downward.

Problem 9

Question: Rotate the given figure three times, each by 90 degrees counterclockwise, around the red point. Draw the final shape.

Solution:

1. First rotation (90 degrees counterclockwise):

   • The triangle shifts to the left of the red dot.
   • The vertical line rotates to the top.
   • The arrow points to the left.

2. Second rotation (90 degrees counterclockwise):

   • The triangle shifts below the red dot.
   • The vertical line rotates to the left.
   • The arrow points downward.

3. Third rotation (90 degrees counterclockwise):

   • The triangle shifts to the right of the red dot.
   • The vertical line rotates downward.
   • The arrow points to the right.

The final shape places:

• The triangle to the right,
• The vertical line below,
• The arrow pointing to the right.

Let me know if you want detailed diagrams for these solutions!

5 Related Questions:

1. What is the general rule for finding the degree of symmetry in regular polygons?
2. How do you determine the direction of rotation (clockwise or counterclockwise)?
3. Can you find the rotational symmetry of any figure without drawing?
4. How many degrees are in a full rotation, and how does that help with solving rotation problems?
5. What happens to the coordinates of a point after a 90-degree rotation around the origin?

Tip:

To visualize rotations effectively, use graph paper and mark key points of the shape before and after rotation.