# Diédrico System: Distance from a point to a line

We can define the distance from a point P to a line r as the smallest of the distances from the point P to the infinite points on the line r. To determine this distance must obtain the line perpendicular to the line r from the point P and get their point of intersection I. The distance d from P to R is the minimum distance from this point to the line r.

This problem can have two different approaches to determining the solution sought.

# System dihedral: Fundamentals of auxiliary projections, changes in plane

To represent an object in the dihedral system usually use the projections on the three planes of the reference trihedron, as we have seen when studying the fundamentals of dihedral system.

In general it is sufficient to use only two of the three possible planes, It is represented for example by a straight projections on the horizontal plane and the vertical. Sometimes it may be desirable, or even necessary, obtain new projections in different directions projection, in which case the call her “auxiliary projections” .

# Diédrico System: Distance from a point to a plane

We can define the distance from a point P to a α as the smallest of the distances from the point P up to the infinite points of the plane α. To determine this distance we get the straight perpendicular to the plane α from the point P and I get your point of intersection. The distance from P to I will be the minimum distance to the plane α.

# Perpendicular to a plane

One of the basic problems that we learn by studying the systems of representation are those in which there are elements that are perpendicular to other. All the problems of determining distances make use of these concepts.

Let's see how to determine the line perpendicular to a plane in dihedral system working directly on the main system projections.

# Fall line

By studying the true magnitude of a line we saw that we could turn calculate the angle of this line with respect to a projection plane, namely, its slope.

In a plane we can determine endless lines with different direction contained therein. One of these lines form the maximum angular condition with respect to the projection plane.

# Diédrico System: Straight lines in a plane parallel to the projection

Under the so-called category “notable lines” plane are those that are parallel to the planes of projection diedricos. These lines are very useful in the operation that we will develop in this system of representation.

# Diédrico System: Theorem of the three perpendicular

One of the most important theorems of descriptive geometry is the so-called “Theorem of the three perpendicular”, It establishes a relation between two lines perpendicular when one of them is parallel to a plane of projection.

# Diédrico System: Projection of the plane

A plane is determined by three unaligned points, so adding a new point to a straight line projections can define it. In this case we will give at least two related dimensions on each plane of projection in order to become independent projections of these plans support of representation. We will learn to represent maps and items belonging to them.

# Diédrico System: True magnitude of the line

By projecting a straight line on a plane orthogonal projection, its projection, generally, is smaller than the original measure.

Given a straight (segment bounded by two points) we want to determine its true magnitude and the angle it makes with the planes of projection.

# Diédrico System: Third straight projection

The main projections on two planes straight dihedral (horizontal and vertical planes) possible to determine other new planes orthogonal projections on.

We'll see how generically determine a new projection from two. Later we will consider your application to study the so-called “auxiliary projections”, influencing their usefulness in solving various problems.

# Diédrico System: Projection of the line

After seeing the foundations of Diédrico System, with the projection of a point on two planes orthogonal projection, let's see how you can wean the system of land line as we have two or more points. This system called “Free System” is more flexible than the traditional because Monge, giving prominence to the reference lines and guiding the conceptual model to a more constructive and less spatial geometry.