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The problem is asking to find the image of the line \( y + 2x - 4 = 0 \) when rotated by \(-90^\circ\) around the origin \((0, 0)\).

### Steps to solve:

1. **Rewrite the line equation in slope-intercept form**:
   \[
   y = -2x + 4
   \]
   This has a slope of \(-2\) and a y-intercept of 4.

2. **Understand rotation of points**:
   When a point \((x, y)\) is rotated counterclockwise by \(-90^\circ\) (which is clockwise), the transformation is given by:
   \[
   (x', y') = (y, -x)
   \]

3. **Transform the line under rotation**:
   To rotate the entire line, substitute each point \((x, y)\) on the line and apply the transformation.

   Since the original equation is \( y = -2x + 4 \), substitute into the rotation formula:
   - The original line: \( y = -2x + 4 \)
   - Rotation by \(-90^\circ\): Each point on the line \( (x, y) \) transforms to \( (y, -x) \).

4. **Apply the transformation**:
   - The new \(x'\) will be the old \(y\), and the new \(y'\) will be the negative of the old \(x\).

   This leads to the transformed equation:
   \[
   x' = -2y' + 4
   \]
   Rearranging for standard linear form, the equation becomes:
   \[
   x' + 2y' - 4 = 0
   \]

Thus, after a \(-90^\circ\) rotation around the origin, the image of the line is:
\[
x + 2y - 4 = 0
\]

Would you like any further clarifications or details on this solution?

Here are 5 related questions to expand on the topic:
1. How do rotations affect the slopes of lines in general?
2. What is the transformation matrix for a \(+90^\circ\) rotation around the origin?
3. How would the line change if rotated by \(180^\circ\) instead?
4. Can the rotation of more complex curves (e.g., circles or parabolas) be handled similarly?
5. How does translation affect a line differently compared to rotation?

**Tip**: Understanding transformations geometrically can make it easier to visualize how shapes and lines behave under rotation or translation.

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

Learn how to find the image of the line y + 2x - 4 = 0 under a -90° rotation around the origin. This detailed solution covers the transformation of coordinates and the resulting linear equation. Suitable for high school students in Grades 10-12.

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