Question

prove section formula for internal division

Answer 1

Section Formula for Internal Division

Let us take a line with two end points A(x1, y1) and B(x2, y2). Consider a point P(x, y) which can divide the given line. Based on the presence of point P, we have two types of section formula.
Section formula for internal division:
If a point P, divides the line internally, we have the following formula.

Representation of section formula for internal division:

Example: 1
Write the coordinate of the point P when it divides the line AB internally in the ratio of 2:3 where A(x1, y1) = (5, 3) and B(x2, y2) = (7, 9).
Solution:
Given:
(x1, y1) = (5, 3)
(x2, y2) = (7, 9 )
m : n = 2 : 3