Section Formula

Introduction

Section formula is the formula of mathematics that is used to find the coordinates of a line in a ratio form.  The formula is widely used in mathematics as well as physics to find the coordinates value of different line segments. In mathematics, it is used to find the “executor” of triangles as well as “centroid” and “incentres”. In this topic, we will discuss the concept of the Section formula. In addition, also elaborate the use of section formula in 3D is here. The analysis of the internal section formula will also be done on this topic. At last, a few FAQs are discussed for the detailed analysis of the Section formula.

What are section formulae in mathematics?

According to the section formula, when a particular point divides a segment of the line in some ratio then the section formula of mathematics is used to find the coordinates of the point that divides the line segment between a certain amount of ratio or the ratio itself. The section formula can be used in finding the midpoint of a line segment. The section formula can be also used in the divination of any line segment into the desired ratio. The section formula is also used to derive the formula of the midpoint in mathematics. The mathematical term of section formula is “section formula” = “P (X, Y)” = “[{(mx2 + nx1)} / (m + n)}, {(my2 + ny1) / (m + n)}]”. Along with this, in this formula ‘m’ and ‘n’ is defined as a line segment that is in the ratio of ‘m: n’,

The section formula is derived in terms of mathematics using two right triangles and by using angle-angle (AA) similarity. The length of the slides of the triangle has been determined in terms of ratio and then solved it in X and Y coordinate, the point is derived that divides the line segment. In the coordinate geometry, the section formula is derived into two sub formulas, is “internal section formula” and the “external section formula”. 

Section formula in 3D

According to the 2-dimensional geometry, the coordinates can be determined regarding the 2-dimensional coordinates. The section formula allows determining the three-dimensional coordinates in the geometry and it helps in the different real-time conditions. The pilots in the aeroplane determine their position using the algorithm of section formula in three-dimensional coordinates. Pilots also used this formula to take their flight towards their destination. Along with this scientist also uses the section formula to send the man-made satellites or other objects in the space that aligns the 3d geometry. Like two dimensions, coordinates to a point in 3D can also be given. The three dimensions are “X-axis”, “Y-axis”, and “Z-axis”, which means the coordinates of a point in 3D will be (X, Y, Z). Taking an example, a cricketer hits the ball then it goes high in the sky. The position of the ball and its distance is determined by using the coordinates and section formula. The section formula of 3D is “section formula” =” P (X, Y, Z)” = “[{(mx2 + nx1)} / (m + n)}, {(my2 + ny1) / (m + n)}, {(mz2 + nz1) / (m + n)}].

Internal section formula

The external section formula is mainly used when a line segment has been divided internally using a point that is given in the desired ratio. The external action formula is used to determine the coordinates of a particular point that is placed between the two points and a line segment is joining these two points in a given ratio. It means a line segment is “AB” is divided by a point “P(X, Y) internally and stand in ratio “AP: PB” = “m: n”. It means the coordinates of the point P is “A(X1, Y1)”, B(X2, Y2)

In the term of the given ratio and the coordinates that are given in the point. So the “internal section formula” = “P (X, Y)” = “[{(mx2 + nx1)} / (m + n)}, {(my2 + ny1) / (m + n)}]”,

where “X” and “Y” are considered as the coordinates of point ‘P’, (X1, Y1) are considered as Cartesian coordinates of the point ‘A’. Same as Point ‘A’, (X2, Y2) are considered as Cartesian coordinates of the point ‘B’. ‘m’ and ‘n’ are the values of ratio in which ‘P’ divides the line in an internal way.

Conclusion

The above topic provided a deep analysis of the section formula. In this topic, the concept of section formula according to mathematics has been analyzed here. The section formula in 3D and its use has been explained here. The internal sectional formula of the section formula has been explained here with its mathematical formula. At last, a few FAQs have also been discussed in this topic for the detailed analysis and its application of real life for the proper analysis of the topic section formula.