Class 10 Mathematics – Equidistant Points

1. What Are Equidistant Points?

• Equidistant points are points that are at the same distance from a given point or line.

• “Equidistant” literally means equal distance.

• These points form a circle (from a point) or parallel lines (from a line) in geometry.

2. Conceptual Understanding

• Imagine standing at a lamp post:

  • All points that are exactly 5 meters away from the lamp post are equidistant from it.

  • On a coordinate plane, these points form a circle centered at the given point.

• Similarly, points equidistant from a line form parallel lines on both sides of the given line.

3. How to Identify Equidistant Points on a Coordinate Plane

1. Identify the reference point or line.

2. Check the distance of other points from this reference.

3. If the distance is the same for all points, they are equidistant.

4. Points forming a symmetrical pattern around the reference are often equidistant.

4. Applications of Equidistant Points

• Constructing circles in geometry.

• Designing boundaries or safe zones around a point.

• Finding central positions or symmetry in layouts.

• Useful in coordinate geometry problems, e.g., locating points that satisfy distance constraints.

5. Key Points to Remember

• Equidistant = same distance from a reference.

• Can be from a point → forms a circle.

• Can be from a line → forms two parallel lines.

• Important in geometry, coordinate geometry, and constructions.

• Helps in problems related to symmetry, distance, and positioning.