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The problem asks you to construct the locus of points that are 4 cm from the line \( MN \) using a ruler and compass only. Here's the procedure to solve it geometrically:

### Step-by-Step Construction:
1. **Draw Parallel Lines**: 
   - Use a ruler to draw the given line \( MN \) clearly.
   - Set your compass to a 4 cm radius.
   - Place the compass point on a point on line \( MN \), and draw an arc on both sides of the line, creating two points above and below.
   - Repeat this process for multiple points along \( MN \) to create two smooth curves that are parallel to \( MN \) and 4 cm away from it.
   
2. **Mark Points at 4 cm Distance**:
   - The two parallel lines that you have drawn, one above and one below the line \( MN \), represent the locus of points that are exactly 4 cm from the line.

3. **Show Construction Arcs**:
   - Keep all your construction arcs visible to show how you obtained the locus.

### Explanation:
The locus of points that are 4 cm from a straight line is two lines parallel to the original line and at a distance of 4 cm above and below it. This is because the set of points at a fixed distance from a line forms parallel lines.

Would you like further clarification on any step?

### Related Questions:
1. What is the geometric definition of a locus?
2. Why are parallel lines formed when constructing loci around a straight line?
3. How can you verify that the distance is exactly 4 cm?
4. What is the importance of keeping construction arcs visible?
5. How would the locus change if the distance was increased to 5 cm?

**Tip**: Always double-check your compass settings when constructing to ensure accuracy in your loci.

Construct the locus of points that are 4 cm from the line MN using a ruler and compasses only. Show all your construction arcs.

Learn how to construct the locus of points that are exactly 4 cm away from a given line using a ruler and compass. This geometry problem focuses on the concept of loci and involves creating parallel lines. Suitable for students in Grades 8-10.

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