Question

How to visualize a section formula through area. Because I do not able to understand in byju's tablet clearly.

Answer 1

The section formula tells us the coordinates of the point which divides a given line segmentinto two parts such that their lengths are in the ratio .

The midpoint of a line segment is the point that divides a line segment in two equal halves. The section formula builds on it and is a more powerful tool; it locates the point dividing the line segment in any desired ratio.

The section formula is helpful in coordinate geometry; for instance, it can be used to find out the centroid, incenter and excenters of a triangle. It has applications in physics too; it helps find the center of mass of systems, equilibrium points, and more.

Section Formula:(Internally)
To find the coordinates of the point which divides internally the line segment joining two given points (x₁,y₁) and (x₂,y₂) in the given ratio m:n

Let A and B be the given two points (x₁,y₁) and (x₂,y₂)respectively.
Then the formula to find the point which is dividing the line-segment AB internally in the ratio m:n is given by





SectionFormula:(Externally)

To find the coordinates of the point which divides Externally the line segment joining two given points (x₁,y₁) and (x₂,y₂) in the given ratio m:n

Let A and B be the given two points (x₁,y₁) and (x₂,y₂)respectively.
The formula which is used to find the point which divides the line-segment AB externally in the ratio m:n is given by