Distance Formula

The distance formula considers as an algebraic expression of mathematics that gives the measurement of the distance between two points or two objects.  The distance formula can be derived from the theorem provided by the Pythagoras. There are two types of distance formula that are generally used to find the distance. One is 2-dimensional and the other is the 3-dimensional formula. In this topic, the calculation of distance using the distance formula has been explained here. The difference between the physical distance and theoretical distance will be shown in this topic. At last, a few FAQs will also be discussed for an effective analysis of the distance formula.  

Discussion

What is the distance formula in mathematics?

The distance formulae are those formulas in mathematics that are mainly used to find the space between the two points or two objects situated in a 2-dimensional plane or 3-dimensional plane. The distance formula is obtained from the Pythagoras theorem. The Pythagorean theorem can also be used to find the distance formula between “a point and a line in 2D”,  “distance between two parallel lines in 2D”, “the shortest distance between the two skew line”, “distance between a point and a plain”, “ distance between two parallel planes”, and so on. The distance formula based on two-dimensional space if the given points are (P, Q) and (R, S) is given as √({(P)2 – (R)2}+ {(Q)2 – (S)2}), and the distance formula is based on three-dimensional formula if the distance between the point (P, Q, R) and (S, T, U) is √{(P – S)2+ (Q – T)2+(R – U)2}.  The distance formula is applied in other areas of mathematics as well as in real-life situations. The distance between the two points of the sea can be determined by identifying the geographical coordinates of those two points and then the distance formula can be applied to find the distance between them. The magnitude formula can be derived with the help of the distance formula to derive the magnitudes of any vectors. 

How to calculate distance using this formula

Accordion g to the Pythagorean Theorem the distance between two points can be derived with the help of the distance formula. For one-dimensional plane first taking the coordinates of two numbers X1 and X2,  if the distance is found in two dimensional then the needed value of (X, Y) points will be (X1, Y1) and (X2, Y2), and for three dimensional the needed values of the points (X, Y, Z) will be (X1, Y1, Z1) and (X2, Y2, Z2). For one-dimensional distance simply need to subtract X2 from to determine the distance between X1 and X2 (D = X2 – X1). To find the distance of two-dimensional coordinates the distance between the points can be simply determined by the formula “D = √{( X2 – X1)2 + (Y2 – Y1)2}”, For example, X1 is 3 and X2 is 11 and Y1 is -10 and Y2 is 7. According to formulas √{(11 – 3)2 + (7 -(-10))2} = √ (64 + 289) = √ (353) = 18.79

To find the distance of the coordinates of three-dimensional planes simply just need to modify the two-dimensional formula and an extra dimension Z is needed. The three-dimensional formula to determine the distance is D = √ {(X2 – X1)2 + (Y2 – Y1)2 + (Z2 – Z1)2}. The three-dimensional formula can determine the distance between the object moving in the space. 

Difference between physical distance and theoretical distance

Physical distance can be considered as a real-time distance, which is an actual space of a length between two points or two objects in a two-dimensional plane or three-dimensional plane. The physical It is a scalar quantity and it is found to form any structure or ant construction. The physical distance is used to find the distance between the cities or mainland. The physical distance may change according to geographic features or factors. It is used to determine how close or how far an object is with respect to another object or point or plane. On the other hand, theoretical distance is a theoretical value of the distance of any scalar quantity.  In mathematics, one matrix palace is considered as a set and theoretical distance refers to the space between those sets. Like this many other distances are determined with the help of the theoretical distance formula. The theoretical distance does not change its value according to geographical factors because it is derived from a particular theory of mathematics. The graphical theories use the theoretical distance to find the space between two points. In human geography, the theoretical distance is used as a subjective experience but not as an objective matrix. It is also used in psychology and social science as an objective matrix.

Conclusion

In the above topic, the distance formula of mathematics has been elaborated. The concept of the distance formula and its driven source has been explained here. The process of calculating the distance using the distance formula in the 2D and 3D planes has been briefed in this context. The difference between theoretical distance and physical distance has been shown here. At last, a few FAQs have been discussed for a better analysis of the topic.