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The problem asks to find the transformed equation of the line \( y + 2x - 4 = 0 \) after being rotated by \(-90^\circ\) around the point \( (0, 0) \).

### Step-by-step solution:

1. **Original Line Equation**: 
   The equation of the line is:
   \[
   y + 2x - 4 = 0 \quad \text{or} \quad y = -2x + 4
   \]

2. **Rotation by \(-90^\circ\)**:
   The rotation matrix for a \(-90^\circ\) rotation is:
   \[
   \begin{pmatrix}
   x' \\
   y'
   \end{pmatrix}
   =
   \begin{pmatrix}
   0 & 1 \\
   -1 & 0
   \end{pmatrix}
   \begin{pmatrix}
   x \\
   y
   \end{pmatrix}
   \]
   This gives the transformations:
   \[
   x' = y \quad \text{and} \quad y' = -x
   \]

3. **Substitute the transformations**:
   Replace \(x\) and \(y\) in the original equation with the new coordinates \(x' = y\) and \(y' = -x\):
   \[
   (-x') + 2(y') - 4 = 0
   \]
   Simplifying this:
   \[
   -x' + 2y' = 4
   \]
   So, the transformed equation of the line after a \(-90^\circ\) rotation is:
   \[
   -x' + 2y' = 4
   \]

Would you like further details or have any questions?

### Related Questions:
1. How does the transformation matrix for \(90^\circ\) rotation differ?
2. How do you generalize the rotation of lines for any angle?
3. What happens if the rotation occurs around a point other than the origin?
4. How do reflections differ from rotations in terms of transformation matrices?
5. How would the equation change if rotated by \(180^\circ\)?

**Tip**: Always check the signs in rotation transformations, especially when dealing with negative angles, as they reverse direction!

Tentukan peta garis y + 2x - 4 = 0 jika dirotasi pada titik (0, 0) sejauh -90°.

Learn how to find the transformation of the line y + 2x - 4 = 0 when rotated by -90 degrees around the origin. This problem involves coordinate geometry, rotations, and solving linear equations. Suitable for high school students in Grades 10-12.

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