https://file.aiquickdraw.com/mathbot/file/17260301202348eaim3jg.jpg

Yes, the image appears to show the result of a 180° counterclockwise rotation about the origin, and the orange triangle seems to be the image of the green triangle after this transformation. Let's check the vertices to confirm this.

The original vertices of the green triangle are:
- \( (1, 3) \)
- \( (2, 1) \)
- \( (3, 2) \)

For a 180° rotation about the origin, the rule is:
\[
(x, y) \rightarrow (-x, -y)
\]

Applying this rule to the vertices:
- \( (1, 3) \rightarrow (-1, -3) \)
- \( (2, 1) \rightarrow (-2, -1) \)
- \( (3, 2) \rightarrow (-3, -2) \)

Now, let's compare these results with the coordinates of the orange triangle's vertices from the image:
- \( (-2.1, -0.9) \)
- \( (-3.2, -1.9) \)
- \( (-0.9, -3) \)

These points are quite close to the expected rotated coordinates, considering possible rounding in the image software. Therefore, it looks correct overall.

Would you like more details on rotation or have any other questions?

### Related Questions:
1. What are the coordinates of the image after a 90° counterclockwise rotation?
2. How does a 180° rotation affect the orientation of the triangle?
3. What is the formula for rotating any point about the origin by 90°, 180°, or 270°?
4. Can you explain the concept of rotational symmetry for geometric shapes?
5. How would you reflect the triangle across the x-axis instead?

**Tip:** When rotating a point 180° around the origin, both the x and y coordinates change their signs.

Learn how to rotate a triangle 180° counterclockwise about the origin. This example covers the mathematical concept of rotation, including applying the transformation formula to the vertices of the triangle. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation