In mathematics as algebra and geometry give the task of finding the distance from a point or a straight line from the specified object.It is completely different ways, the choice of which depends on the source data.Here's how to find the distance between the specified objects in different conditions.
use of measuring instruments
At the initial stage of development of mathematical science are taught how to use basic tools (such as a ruler, protractor, compass, triangle, etc.).Find the distance between points or lines by means of them is a snap.Enough to make the scale of divisions and write the answer.One only has to know that the distance is equal to the length of the straight line can be drawn between the points, as in the case of parallel lines - perpendicular between them.
use of theorems and axioms of geometry
In high school, learn to measure the distance without using special tools or graph paper.This requires numerous theorems, axioms and proofs.Often, the problem of how to find the distance reduced to the formation of a right triangle and the search for his party.To solve these problems need to know the Pythagorean theorem, properties of triangles and methods of conversion.
points on the coordinate plane
If there are two points and given their position on the coordinate axes, then how to find the distance from one to the other?The solution will involve several stages:
- Putting points on the line, the length of which will be the distance between them.
- find the difference between the coordinate values of the points (a, p) each axis: | k1 - k2 | = d1 and | p1 - p2 | = q2 (values take modulo, because the distance can not be negative).
- Then erect get the number of the square and find their sum: D12 + d22
- The final stage will be the square root of the resulting number.This will be the distance between the points: d = V (D12 + d22).
As a result, the entire solution is carried out by a single formula, where the distance is equal to the square root of the sum of squared differences of coordinates:
d = V (| k1 - k2 | 2+ | p1 - p2 | 2)
If you have a questionhow to find the distance from one point to another in three-dimensional space, the search for an answer to it will not be particularly different from the above.The decision will be based on the following formula:
d = V (| k1 - k2 | 2+ | p1 - p2 | 2+ | E1 - E2 | 2)
Parallel lines
perpendicular drawn from any point lyingon a straight line parallel to, and will distance.When solving problems in a plane you need to find the coordinates of any point of one of the lines.And then calculate the distance from it to the second line.To do this, we give them to the general equation line of the form Ax + By + C = 0.From the known properties of parallel lines that their coefficients A and B are equal.In this case, find the distance between parallel lines can be defined as:
d = | C1 - C2 | / V (A2 + B2)
Thus, in answering the question of how to find the distance from the target object should be guided by the conditionchallenges and provide the tools to address it.They can be as measuring devices and theorems and formulas.
