Add your company website/link

to this blog page for only $40 Purchase now!

Continue

A free tool that can help you determine the word count per hour required!

Here is when the concept of perpendicular line becomes crucial. The distance between a point and a continuous object is defined via perpendicularity. From a geometrical point of view, the first step to measure the distance from one point to another, is to create a straight line between both points, and then measure the length of that segment. When we measure the distance from a point to a line, the question becomes "Which of the many possible lines should I draw?". In this case the answer is: the line from the point that is perpendicular to the first line. This distance will be zero in the case in which the point is a part of the line. For these 1D cases, we can only consider the distance between points, since the line represents the whole 1D space.The length of a segment is usually denoted by using the endpoints without an overline. For instance, the `\text{length of AB}` is denoted by `\overline{AB}` or sometimes `m\overline{AB}`. A ruler is commonly used to find the the distance between two points. If we place the `0` mark at the left endpoint, and the mark on which the other endpoint falls on is the distance between two points. In general, we do not need to measure from the 0 mark. By the ruler postulate, the distance between two points is the absolute value between the numbers shown on the ruler. On the other hand, if two points `A and B` are on the x-axis, i.e. the coordinates of `A and B` are `(x_A,0)` and `(x_B,0)` respectively, then the distance between two points `AB = |x_B −x_A|`. The same method can be applied to find the distance between two points on the y-axis. The formula for the distance between two points in two-dimensional Cartesian coordinate plane is based on the Pythagorean Theorem. So, the Pythagorean theorem is used for measuring the distance between any two points `A(x_A,y_A)` and `B(x_B,y_B)` (S\Here, we have inadvertently risen a fascinating point, which is that we measure distances not in length but in time. Thus, we extend the notion of distance beyond its geometrical sense. We will explore this possibility in the next section as we speak about the importance and usefulness of distance beyond the purely geometrical sense. This is a very interesting path to take and is mostly inspired by the philosophical need to extend every concept to have a universal meaning, as well as from the obvious physical theory to mention, when talking about permutations of the space and time, or any other variable that can be measured.

Typically, the concept of distance refers to the geometric Euclidean distance and is linked to length. However, you can extend the definition of distance to mean just the difference between two things, and then a world of possibilities opens up. Suddenly one can decide what is the best way to measure the distance between two things and put it in terms of the most useful quantity. A very simple step to take is to think about the distance between two numbers, which is nothing more than the 1D difference between these numbers. To obtain it, we simply subtract one from the other and the result would be the difference, a.k.a. the distance. By extending the concept of distance to mean something closer to difference, we can calculate the difference between two temperatures in terms of degrees or thermal energy, or other related quantity like pressure. But we don't need to get really extreme, let's see how two points can be separated by a different distance, depending on the assumptions made. Coming back to the driving distance example, we could measure the distance of the journey in time, instead of length. In this case, we need an assumption to allow such translation; namely the way of transport.There is a big difference in the time taken to travel 10 km by plane versus the time it takes by car; or by car versus bike. Sometimes, however, the assumption is clear and implicitly agreed on, like when we measure the lightning distance in time which we then convert to length. This brings up an interesting point, that the conversion factor between distances in time and length is what we call speed or velocity (remember they are not exactly the same thing). Truth be told, this speed doesn't have to be constant as exemplified by accelerated motions such as that of a free fall under gravitational force, or the one that links stopping time and stopping distance via the breaking force and drag or, in very extreme cases, via the force of a car crash. (Source: www.omnicalculator.com)