https://file.aiquickdraw.com/mathbot/file/17268968144913b4jqpgm.jpg

The problem asks for the **sequence of transformations** applied to the blue triangle to obtain the red triangle. Let's break down the transformations step by step:

1. **Identify Points**:
   - The blue triangle has vertices at \( A(1, 4) \), \( B(3, 4) \), and \( C(2, 6) \).
   - The red triangle has vertices at \( A'(-2, -4) \), \( B'(-4, -4) \), and \( C'(-3, -6) \).

2. **Reflection**:
   - Notice that the signs of the x-coordinates and y-coordinates are reversed between the blue and red triangles.
   - This suggests a **reflection over the origin** (a 180-degree rotation or a reflection over both the x-axis and y-axis).

3. **Rotation**:
   - After the reflection over the origin, you can check the distances between corresponding points to verify that this transformation alone gives us the new positions. The reflection effectively rotates the triangle 180 degrees around the origin.

Thus, the sequence of transformations is:

1. **Reflection over the origin** (which is equivalent to a 180-degree rotation).

Would you like more details on the process, or do you have any questions?

Here are 5 related questions:
1. What is the difference between reflection and rotation in geometry?
2. How can you identify a transformation on a coordinate grid?
3. What is the mathematical definition of a 180-degree rotation?
4. How do you reflect a shape over the x-axis or y-axis alone?
5. What other transformations could change the orientation of a triangle?

**Tip**: To quickly identify reflections, check if the signs of coordinates are inverted across a line (such as the x-axis, y-axis, or origin).

What is the sequence of transformations for the image given?

Understand the sequence of transformations for geometric shapes on a coordinate plane. This example explains how to identify transformations such as reflection and rotation between two triangles. Suitable for students in Grades 7-9.

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