The locus of a point which moves so that it is equidistant from two intersecting straight lines is the?

Analysis

The question asks for the geometric path (locus) traced by a point that maintains an equal distance from two lines that intersect at a point.

Concept: Locus of Points

In geometry, a locus is the set of all points that satisfy a specific condition.

1. When you have two intersecting lines, they form angles at the point of intersection.
2. Any point that is equidistant from two intersecting lines must lie on the line that divides the angle between those two lines into two equal parts.
3. This line is mathematically referred to as the angle bisector.

Step-by-Step Solution

1. Visualize the lines: Imagine two lines crossing each other like an "X".
2. Define the condition: We are looking for a point $P(x, y)$ such that the perpendicular distance from $P$ to Line 1 is equal to the perpendicular distance from $P$ to Line 2.
3. Apply the property: By the Angle Bisector Theorem, the set of all points equidistant from two intersecting lines forms the bisector of the angles formed by those lines.
4. Evaluate the options: • A perpendicular bisector is used for a line segment, not two intersecting lines. • A line parallel to the two lines would not be equidistant to both simultaneously. • The "angle bisector" is the precise geometric term for this locus.

Conclusion

The locus of a point equidistant from two intersecting lines is the angle bisector of the two lines. This ensures that for any point chosen on this bisector, the perpendicular distance to both original lines remains identical.

Exam Tip

Whenever you see the word "equidistant" in a locus question:

• If it is from two fixed points, the locus is the perpendicular bisector.
• If it is from two intersecting lines, the locus is the angle bisector.