It seems like the image contains geometry problems related to rotations on a coordinate plane. Let's go through each problem one by one:

1. Problem 7 involves rotating the trapezoid $QRST$ 90° clockwise. Given the points:

   • $Q(2, 1)$
   • $R(2, 5)$
   • $S(4, 5)$
   • $T(8, 1)$

   To rotate a point 90° clockwise around the origin (0, 0), the formula is: $(x, y) \to (y, -x)$

   Applying this formula to each of the points:

   • For $Q(2, 1)$, the new coordinates will be $Q'(1, -2)$.
   • For $R(2, 5)$, the new coordinates will be $R'(5, -2)$.
   • For $S(4, 5)$, the new coordinates will be $S'(5, -4)$.
   • For $T(8, 1)$, the new coordinates will be $T'(1, -8)$.

2. Problem 10 asks for the coordinates of point $T$ after a 180° rotation about the origin. The rotation rule for 180° is: $(x, y) \to (-x, -y)$ If the coordinates of $T$ are given as $T(8, 1)$, applying the rotation rule:

   • $T'( -8, -1)$

3. Problem 11 asks for the coordinates of point $G$ after a 90° counterclockwise rotation about the origin. The formula for a 90° counterclockwise rotation is: $(x, y) \to (-y, x)$ If the coordinates of $G$ are given, apply the rule to get the new position.

4. Problem 13 involves the coordinates of point $P(8, -2)$ after a 180° rotation. The formula for a 180° rotation is: $(x, y) \to (-x, -y)$ So, $P'( -8, 2)$.

5. Problem 14 involves rotating point $M(-5, -4)$ 90° counterclockwise. Using the 90° counterclockwise formula: $(x, y) \to (-y, x)$ The coordinates of $M'$ will be $M'( -4, -5)$.

If you'd like to go into more detail on how each of these transformations work or have any specific questions, feel free to ask!

Here are some related questions that you may find interesting:

1. How does a 270° rotation differ from a 90° or 180° rotation?
2. How can we calculate the rotation of a figure other than points (e.g., polygons)?
3. What are some other transformations besides rotation, such as translation or reflection?
4. How do you apply rotations to figures that are not centered at the origin?
5. How do you rotate shapes in 3D space?

Tip: Always keep in mind the order of the transformations and the center of rotation when solving these types of problems!