https://file.aiquickdraw.com/mathbot/file/1726789184760hdh47xqz.jpg

The image you uploaded shows a coordinate plane with a rectangle whose vertices are labeled \(D\), \(E\), \(F\), and \(G\). You are asked to determine the coordinates of these points after a 90° counterclockwise rotation about the origin.

### Rotation Rule for 90° Counterclockwise:
For a point \((x, y)\), the coordinates after a 90° counterclockwise rotation around the origin become:
\[
(x', y') = (-y, x)
\]

Now, let’s apply this rule to each vertex:

1. **Point \(D\)**:
   - Original coordinates: \((-7, 1)\)
   - After rotation: \((-1, -7)\)

2. **Point \(E\)**:
   - Original coordinates: \((-7, 6)\)
   - After rotation: \((-6, -7)\)

3. **Point \(F\)**:
   - Original coordinates: \((-3, 6)\)
   - After rotation: \((-6, -3)\)

4. **Point \(G\)**:
   - Original coordinates: \((-3, 1)\)
   - After rotation: \((-1, -3)\)

### Coordinates after 90° counterclockwise rotation:
- \(D' = (-1, -7)\)
- \(E' = (-6, -7)\)
- \(F' = (-6, -3)\)
- \(G' = (-1, -3)\)

Would you like further clarification or details on how this transformation works? 

Here are some related questions to deepen your understanding:
1. How would you rotate a point 180° about the origin?
2. What changes when you rotate a point 90° clockwise instead of counterclockwise?
3. How would the coordinates change if the rotation was 270° counterclockwise?
4. Can you describe how to reflect a point across the y-axis?
5. How would you perform a translation instead of a rotation for these points?

**Tip:** For geometric transformations, visualizing the grid and tracing points can help confirm your answers.

Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.

Learn how to rotate points on a coordinate plane by 90° counterclockwise around the origin. This example problem involves finding the new coordinates of the vertices after the rotation. Ideal for students in Grades 8-10.

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