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Describe a sequence of transformations that maps triangle abc onto triangle a’b’c’

To map triangle \(ABC\) to triangle \(A'B'C'\), we need to describe the sequence of transformations. From the image, we can observe the following:

1. **Original Points (Triangle ABC)**:
   - \(A(2, -7)\)
   - \(B(6, -5)\)
   - \(C(0, 2)\)

2. **Transformed Points (Triangle A'B'C')**:
   - \(A'(-4, -1)\)
   - \(B'(-6, -3)\)
   - \(C'(-3, 1)\)

### Sequence of Transformations:

#### Step 1: **Rotation by 90° clockwise**
   - Rotating triangle ABC by 90° clockwise around the origin will move the points as follows:
     - \(A(2, -7) \to A'(-4, -1)\)
     - \(B(6, -5) \to B'(-6, -3)\)
     - \(C(0, 2) \to C'(-3, 1)\)

This rotation explains the transformation from triangle \(ABC\) to triangle \(A'B'C'\).

### Conclusion:
The transformation that maps triangle \(ABC\) onto triangle \(A'B'C'\) is a **90° clockwise rotation** about the origin.

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Would you like further details or have any other questions?

Here are 5 related questions to explore:

1. What are the effects of rotating a shape by different angles (e.g., 180°, 270°)?
2. How does a reflection differ from a rotation in terms of transformations?
3. How can you determine the center of rotation for any given transformation?
4. What are some real-life applications of geometric transformations?
5. What is the difference between clockwise and counterclockwise rotations?

**Tip:** When rotating a figure, positive angles typically indicate counterclockwise rotation, while negative angles indicate clockwise rotation.

Describe a sequence of transformations that maps Triangle ABC onto Triangle A'B'C'.

Learn how to map Triangle ABC onto Triangle A'B'C' through a 90° clockwise rotation about the origin. This problem covers geometric transformations, including rotations and coordinate geometry. Suitable for students in Grades 8-10.

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