https://file.aiquickdraw.com/mathbot/file/1726114917947gs6qgx3a.jpg

To find the new coordinates of the vertices after a rotation, we will apply the appropriate rotation transformation rules:

### 7. Rotation of Trapezoid QRST
- **Rotation**: 90° clockwise.
- **Original vertices**:
  - Q(2, 1)
  - R(2, 5)
  - S(4, 5)
  - T(8, 1)

**Rotation Rule for 90° clockwise**:  
\((x, y) \rightarrow (y, -x)\)

Applying the rule to each vertex:
1. **Q(2, 1)**:  
   New point \(Q'\) = (1, -2)
2. **R(2, 5)**:  
   New point \(R'\) = (5, -2)
3. **S(4, 5)**:  
   New point \(S'\) = (5, -4)
4. **T(8, 1)**:  
   New point \(T'\) = (1, -8)

### 8. Rotation of Triangle MNP
- **Rotation**: 270° clockwise.
- **Original vertices**:
  - M(-7, 6)
  - N(-1, 2)
  - P(-6, 0)

**Rotation Rule for 270° clockwise (equivalent to 90° counterclockwise)**:  
\((x, y) \rightarrow (-y, x)\)

Applying the rule to each vertex:
1. **M(-7, 6)**:  
   New point \(M'\) = (-6, -7)
2. **N(-1, 2)**:  
   New point \(N'\) = (-2, -1)
3. **P(-6, 0)**:  
   New point \(P'\) = (0, -6)

### Final Coordinates:
- **Trapezoid QRST (90° clockwise)**
  - Q' = (1, -2)
  - R' = (5, -2)
  - S' = (5, -4)
  - T' = (1, -8)

- **Triangle MNP (270° clockwise)**
  - M' = (-6, -7)
  - N' = (-2, -1)
  - P' = (0, -6)

Would you like more details or have any questions?

### Related Questions:
1. How do you find the coordinates after a 180° rotation?
2. What is the effect of a 270° counterclockwise rotation on a coordinate?
3. How do you reflect a shape over the x-axis or y-axis?
4. What are the rules for rotating a point 90° counterclockwise?
5. Can you explain how to translate a shape on the coordinate plane?

### Tip:
When rotating shapes on the coordinate plane, remember that rotating clockwise or counterclockwise by 90°, 180°, or 270° has specific rules for swapping and negating coordinates.

Learn how to rotate trapezoid QRST and triangle MNP on a coordinate plane. This exercise involves applying the 90° clockwise and 270° clockwise (equivalent to 90° counterclockwise) rotation rules to find the new coordinates of the vertices. Suitable for students in Grades 7-9.

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