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To solve this problem, we need to find the equation of the line after it is rotated 90 degrees counterclockwise around the origin \((0, 0)\).

### Original Equation of the Line

The original equation is:

\[
2x + y + 3 = 0
\]

### Rotation of a Line by 90 Degrees Counterclockwise

To rotate a line by 90 degrees counterclockwise, we can use the transformation for rotating points:

\[
(x', y') = (-y, x)
\]

Substitute \(x'\) and \(y'\) back into the original line equation. We substitute \(x = y'\) and \(y = -x'\):

\[
2(y') + (-x') + 3 = 0
\]

Simplify this equation:

\[
2y' - x' + 3 = 0
\]

Rewriting it in the standard form \(Ax + By + C = 0\), we have:

\[
-x' + 2y' + 3 = 0
\]

Now, replacing \(x'\) back with \(x\) and \(y'\) back with \(y\):

\[
-x + 2y + 3 = 0
\]

### Conclusion

The equation after rotation is:

\[
\boxed{x + 2y + 3 = 0}
\]

So, the correct answer is:

**D. x + 2y + 3 = 0**

Would you like further clarification or more details? 

Here are some additional related questions you might find interesting:

1. What would be the equation of the line if rotated 180 degrees around the origin?
2. How do you rotate a line 90 degrees clockwise around a point other than the origin?
3. How can we determine the intersection points between the original and the rotated lines?
4. What is the geometric interpretation of rotating a line around the origin?
5. How would the equation change if the line were translated instead of rotated?

**Tip:** When working with rotations, remember that the signs of the coordinates change depending on the direction (clockwise or counterclockwise) and the center of rotation.

Persamaan garis 2x + y + 3 = 0 dirotasikan dengan pusat (0, 0) sebesar 90° berlawanan arah jarum jam. Tentukan persamaan bayangannya.

This solution explains how to find the new equation of a line after rotating it 90 degrees counterclockwise around the origin. The problem involves key geometric concepts, such as coordinate geometry, transformations, and the rotation theorem. Suitable for students in Grades 9-11.

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