To determine the locus of a point that is 5 cm from the line LM, we need to understand what a locus is and how distances from a line work in geometry. ### Correct Option: B. Pair of lines on opposite sides of LM and parallel to it, each distance 5 cm from LM. ### Explanation of the Correct Answer: 1. **Understanding Locus**: - The locus of a point is the set of all points that satisfy a certain condition. In this case, the condition is that the point must be 5 cm away from the line LM. 2. **Distance from a Line**: - The distance from a point to a line is measured perpendicularly. Therefore, if we want to find all points that are 5 cm away from line LM, we need to consider both sides of the line. 3. **Visualizing the Locus**: - Imagine line LM drawn horizontally on a plane. If you take a point that is 5 cm above this line, that point is 5 cm away from LM. Similarly, if you take another point that is 5 cm below the line, that point is also 5 cm away from LM. - Therefore, the locus of all such points forms two lines: one line that is 5 cm above LM and another line that is 5 cm below LM. Both of these lines are parallel to LM. 4. **Conclusion**: - The locus is not just a single line but rather two lines, one on each side of LM, both parallel to it and each at a distance of 5 cm. This is why option B is correct. ### Why the Other Options are Incorrect: - **Option A: A line distance 10 cm from LM and parallel to LM**: - This option suggests that there is only one line that is 10 cm away from LM. However, the problem specifies a distance of 5 cm, not 10 cm. Therefore, this option is incorrect. - **Option C: Line parallel to LM and 5 cm from LM**: - This option implies that there is only one line that is 5 cm away from LM. However, as explained, there are actually two lines (one above and one below LM) that are both 5 cm away. Thus, this option is incomplete and incorrect. - **Option D: Pair of parallel lines on one side of LM and parallel to LM**: - This option suggests that both lines are on the same side of LM. However, the locus includes points on both sides of the line LM, making this option incorrect. ### Summary of Key Points: - The locus of points 5 cm from line LM consists of two lines. - These lines are parallel to LM, one located 5 cm above and the other 5 cm below LM. - The distance from a line is measured perpendicularly, which is crucial for understanding the locus. - The correct answer is option B, as it accurately describes the situation. By understanding these concepts, you can confidently tackle similar problems involving loci and distances in geometry!