if my triangle EFG have the following plots E(-1,-4), F(-3,-4), and G (-4,-4) can you please do a 90 degree rotation?

A 90-degree counterclockwise rotation of a point about the origin transforms any point \((x, y)\) into \((-y, x)\). Let's apply this transformation to each of the vertices of triangle \(EFG\):

1. **E(-1, -4)**:  
   After the rotation, this point becomes:
   \[
   (-(-4), -1) = (4, -1)
   \]

2. **F(-3, -4)**:  
   After the rotation, this point becomes:
   \[
   (-(-4), -3) = (4, -3)
   \]

3. **G(-4, -4)**:  
   After the rotation, this point becomes:
   \[
   (-(-4), -4) = (4, -4)
   \]

So, the new vertices of triangle \(EFG\) after a 90-degree counterclockwise rotation about the origin are:

- \(E'(4, -1)\)
- \(F'(4, -3)\)
- \(G'(4, -4)\)

These points describe a vertically oriented triangle along the line \(x = 4\).

Would you like further details on rotations or any clarifications?

### Follow-up Questions:
1. How would a clockwise 90-degree rotation of the triangle change the coordinates?
2. Can you calculate the area of the original triangle \(EFG\)?
3. What would the triangle look like after a 180-degree rotation?
4. Can you perform a translation on the new triangle \(E'F'G'\)?
5. How do different types of transformations (e.g., translation, reflection) affect the orientation of a shape?

### Tip:
When performing rotations, the origin is often used as the pivot point, but you can also rotate around any point by adjusting your transformation accordingly.

Learn how to perform a 90-degree counterclockwise rotation on triangle EFG with vertices E(-1,-4), F(-3,-4), and G(-4,-4). This geometry problem applies the coordinate transformation formula (x, y) → (-y, x) and is suitable for students in Grades 8-10.

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