Equidistant — Definition, Meaning & Examples
Equidistant
Equally distant. For example, any two points on a circle are equidistant from the center.
Worked Example
Problem: Points A(1, 0) and B(−1, 0) lie on the x-axis. Show that both points are equidistant from the origin O(0, 0).
Step 1: Find the distance from A to O using the distance formula.
OA=(1−0)2+(0−0)2=1=1
Step 2: Find the distance from B to O.
OB=(−1−0)2+(0−0)2=1=1
Step 3: Compare the two distances. Since OA = OB = 1, the points are the same distance from the origin.
OA=OB=1
Answer: A and B are equidistant from the origin because both are exactly 1 unit away.
Why It Matters
The idea of equidistance defines many geometric objects. A circle is the set of all points equidistant from a center, and a perpendicular bisector is the set of all points equidistant from two endpoints of a segment. Recognizing equidistance helps you construct midpoints, bisectors, and loci in both pure geometry and coordinate geometry.
Common Mistakes
Mistake: Assuming two points that look equally far apart on a diagram are truly equidistant without calculating.
Correction: Always verify with the distance formula or a geometric theorem. Visual estimates can be misleading, especially on non-uniform scales.
Related Terms
- Point — The objects measured for equidistance
- Circle — All points equidistant from a center
- Distance Formula — Used to verify equidistance numerically
- Perpendicular Bisector — Locus of points equidistant from two endpoints
- Midpoint — The point equidistant from both ends of a segment