https://file.aiquickdraw.com/mathbot/file/1729389630771uaaoqtic.jpg

The problem asks to find the coordinates of the vertices \( F \), \( G \), and \( H \) after a 90° counterclockwise rotation about the origin.

### Step 1: Identify the initial coordinates of the vertices.
From the graph, the coordinates of the vertices are:
- \( F (-8, 10) \)
- \( G (2, 10) \)
- \( H (-8, 0) \)

### Step 2: Apply the 90° counterclockwise rotation formula.
When a point \( (x, y) \) is rotated 90° counterclockwise around the origin, the new coordinates \( (x', y') \) are given by:
\[
(x', y') = (-y, x)
\]
This means:
- The new \( x' \)-coordinate is the negative of the original \( y \)-coordinate.
- The new \( y' \)-coordinate is the original \( x \)-coordinate.

### Step 3: Calculate the new coordinates.

- For \( F (-8, 10) \):
  \[
  F' = (-10, -8)
  \]
- For \( G (2, 10) \):
  \[
  G' = (-10, 2)
  \]
- For \( H (-8, 0) \):
  \[
  H' = (0, -8)
  \]

### Final Coordinates After Rotation:
- \( F' (-10, -8) \)
- \( G' (-10, 2) \)
- \( H' (0, -8) \)

Would you like further clarification on the rotation process or a different topic?

Here are some related questions for further practice:
1. What is the rule for rotating points 180° around the origin?
2. How would the coordinates change after a 270° clockwise rotation?
3. How do you reflect a point across the x-axis and y-axis?
4. How can you find the coordinates of a point after a translation?
5. How do you perform a dilation of a point with respect to the origin?

**Tip:** When performing a transformation like rotation, it helps to visualize or sketch the new positions of the points on the graph!

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

Learn how to find the coordinates of vertices after a 90° counterclockwise rotation around the origin with a step-by-step solution. This problem covers key concepts in coordinate geometry and transformations, suitable for students in Grades 8-10.

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