# Shortest distance between a point and line segment where two faces meet

### Illustrative Mathematics

Let be the point on so that meets perpendicularly and let be any other point on as Theorem is the cornerstone for evaluating the distance between two points. The true distance between a line and a point is the shortest distance between them. Next, find the point view of the two lines by making a perpendicular folding line Distances at an Angle from the Horizontal, as Applied to Line Segments[edit] distance between a given point and the closest point on the nearest face to. In Geometry also, a ray starts from a point and may go to infinity. It has staring It indicates it can go further on both sides without end. This is It is the shortest path between the two points. A line If the two lines on a plane meet, we say the two lines intersect and the point where they meet is called point of intersection.

### Line segment - Wikipedia

As a degenerate orbit this is a radial elliptic trajectory. In other geometric shapes[ edit ] In addition to appearing as the edges and diagonals of polygons and polyhedraline segments appear in numerous other locations relative to other geometric shapes.

Triangles[ edit ] Some very frequently considered segments in a triangle include the three altitudes each perpendicularly connecting a side or its extension to the opposite vertexthe three medians each connecting a side's midpoint to the opposite vertexthe perpendicular bisectors of the sides perpendicularly connecting the midpoint of a side to one of the other sidesand the internal angle bisectors each connecting a vertex to the opposite side. In each case there are various equalities relating these segment lengths to others discussed in the articles on the various types of segment as well as various inequalities.

Other segments of interest in a triangle include those connecting various triangle centers to each other, most notably the incenterthe circumcenterthe nine-point centerthe centroidand the orthocenter.

Quadrilaterals[ edit ] In addition to the sides and diagonals of a quadrilateralsome important segments are the two bimedians connecting the midpoints of opposite sides and the four maltitudes each perpendicularly connecting one side to the midpoint of the opposite side.

Circles and ellipses[ edit ] Any straight line segment connecting two points on a circle or ellipse is called a chord.

Any chord in a circle which has no longer chord is called a diameterand any segment connecting the circle's center the midpoint of a diameter to a point on the circle is called a radius. In an ellipse, the longest chord, which is also the longest diameteris called the major axis, and a segment from the midpoint of the major axis the ellipse's center to either endpoint of the major axis is called a semi-major axis.

Similarly, the shortest diameter of an ellipse is called the minor axis, and the segment from its midpoint the ellipse's center to either of its endpoints is called a semi-minor axis.

The chords of an ellipse which are perpendicular to the major axis and pass through one of its foci are called the latera recta of the ellipse. The interfocal segment connects the two foci. Directed line segment[ edit ] When a line segment is given an orientation direction it suggests a translation or perhaps a force tending to make a translation.

The magnitude and direction are indicative of a potential change. The sides and arcs are called the edges of the figure.

## Descriptive Geometry/Distances

The edges are one-dimensional, but they lie in the plane, which is two-dimensional. The endpoints of the edges are called the vertices or corners. These points are zero-dimensional, but they also lie in the plane, which is two-dimensional.

The most common figures have only a few edges, the curves are very simple, and there are no "loose ends" - that is, every vertex is the endpoint of at least two edges. If all the edges are segments, every vertex is the endpoint of two sides, and no two sides cross each other, the figure is called a polygon.

Here are some names of polygons. Polygons often divide the plane into two pieces, an inside and an outside. The inside part is called the region enclosed by the figure. The name of the figure is also commonly used for this region, and the area of the region is commonly called the area of the figure. When two sides meet at a vertex, they form an angle.

Actually they form two angles, one inside the figure, and one outside.

**VERY HARD Puzzle: What Is The Distance Between Two Random Points In A Square?**

The one inside is called the interior angle at that vertex, or simply the angle at that vertex. Mathematically speaking, a triangle consists of three vertices and three sides only. The interior is not included. When you want to refer specifically to the interior of a figure that does not have a name of its own, you can call it "the region of the plane enclosed by the figure" or "the figurate region": What is a three-dimensional figure?

A three-dimensional figure, sometimes called a solid figure, is a set of plane regions and surface regions, all lying in three-dimensional space.