Learn the Class 9 Madhyamik Mathematics Internal and External Division of Straight Line Formulas with clear explanations and solved examples. This page covers the Internal Division Formula, Midpoint Formula, and External Division Formula for quick revision and exam preparation.
Chapter 19 – Coordinate Geometry: Internal and External Division | Class 9 Flash Formula
Internal Division Formula
If a point P divides the line joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m : n, then
P = \left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right)
Example :
Find the point dividing the line joining A(2, 4) and B(8, 10) internally in the ratio 1 : 2.
Solution
x-coordinate = 1 × 8 + 2 × 2\over 1 + 2 = 8 + 4\over 3 = 12\over3 = 4
y-coordinate = 1 × 10 + 2 × 4\over 1 + 2 = 10 + 8 \over 3 = 18\over3 = 6
Therefore, coordinate of P = (4, 6)
Mid-point Formula
The midpoint of the line joining A(x₁, y₁) and B(x₂, y₂) is
M = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)
Example :
Find the midpoint of A(2, 4) and B(8, 10).
Solution
x-coordinate = 2 + 8 \over 2 = 10\over 2 = 5
y-coordinate = 4 + 10 \over 2 = 14\over2 = 7
Therefore, coordinate of M = (5, 7)
External Division Formula
If a point P divides the line joining A(x₁, y₁) and B(x₂, y₂) externally in the ratio m : n, then
P = \left(\frac{mx_2-nx_1}{m-n},\frac{my_2-ny_1}{m-n}\right)
Example :
Find the point dividing the line joining A(2, 4) and B(8, 10) externally in the ratio 2 : 1.
Solution
x-coordinate = 2 × 8 − 1 × 2\over 2 − 1 = 16 − 2\over1 = 14
y-coordinate = 2 × 10 − 1 × 4\over 2 − 1 = 20 − 4\over 1 = 16
Therefore, P = (14, 16)
You have reached the end.