Equidistant facts for kids

This red line is a perpendicular bisector. Any point on it is equidistant from the two ends of the black line segment.

The circle goes around the polygon. Its center is equidistant from all the polygon's corners.

When we say a point is equidistant from a group of things, it means the distance from that point to each of those things is exactly the same. Imagine you're standing in the middle of a room. If you are equidistant from all four walls, it means you are the same distance from each wall.

This idea is super important in geometry, which is the study of shapes and spaces.

Equidistance in 2D and 3D Space

In Euclidean geometry, which is the kind of geometry we usually learn in school, we can see equidistance in different ways:

Points and Lines

• If you have two different points, like A and B, the set of all points that are equidistant from both A and B forms a straight line. This line is called the perpendicular bisector of the line segment connecting A and B. It cuts the segment in half and is at a 90-degree angle to it.
• In three-dimensional space, if you have two points, all the points that are equidistant from them form a flat surface called a plane. Think of it like an invisible wall exactly halfway between the two points.

Shapes and Their Centers

• For a circle, its center is equidistant from every single point on the circle's edge. This is the very definition of a circle!
• Just like a circle, the center of a sphere (a 3D ball shape) is equidistant from every point on its surface.
• In a triangle, there's a special point called the circumcentre. This point is equidistant from all three corners (or vertices) of the triangle. You can always draw a circle around any triangle, and its center will be the circumcentre.
• Another special point in a triangle is the incentre. This point is equidistant from all three sides of the triangle. You can draw a circle inside the triangle that touches all three sides, and its center will be the incenter.
• The center of a rectangle is equidistant from all four corners. It's also equidistant from its two opposite long sides, and equidistant from its two opposite short sides.
• If you have two parallel lines (lines that never meet), they are always equidistant from each other. This means the shortest distance between any point on one line and the other line is always the same.

Parabolas

A parabola is a special curve you might see in math or science. It's made up of all the points that are equidistant from a fixed point (called the focus) and a fixed straight line (called the directrix). The distance to the directrix is always measured straight across, at a 90-degree angle.

See also

• Equidistant set