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To rotate the given polygon 90° counterclockwise about the origin, each point \((x, y)\) is transformed using the following rule for 90° rotation counterclockwise:

\[
(x, y) \rightarrow (-y, x)
\]

Let's apply this to each vertex of the polygon:

- Point \(A(-5, 4)\) becomes \(A'(-4, -5)\).
- Point \(B(1, 4)\) becomes \(B'(-4, 1)\).
- Point \(C(1, 0)\) becomes \(C'(0, 1)\).
- Point \(D(-3, 0)\) becomes \(D'(0, -3)\).
- Point \(E(-2, 2)\) becomes \(E'(-2, -2)\).
- Point \(F(-5, 1)\) becomes \(F'(-1, -5)\).

Now you can plot these new points \(A', B', C', D', E', F'\) to form the rotated polygon.

Would you like further clarification or assistance with plotting? Here are some related questions to deepen your understanding:

1. What is the formula for rotating a point 180° about the origin?
2. How would you rotate a point 90° clockwise?
3. What is the relationship between rotation and reflection in transformations?
4. Can you describe how the shape of the polygon changes after the rotation?
5. How can you determine the coordinates of a point after a 270° rotation?

**Tip:** When rotating a point, make sure to carefully apply the transformation rule to avoid errors with signs.

Rotacione 90° o polígono a seguir com relação à origem no sentido anti-horário.

Learn how to rotate a polygon 90° counterclockwise around the origin using coordinate transformations. The problem involves understanding how to apply the transformation formula (x, y) → (-y, x) to each vertex of the polygon. Suitable for students in Grades 9-11.

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