Question

Given three points A(-7, 1), B(m, 6) and P(-1, n). If the point P divides AB internally in the ratio of 3: 2, find the values of m and n.​

Answer 1

m = 3 , n = 4

Explanation:

Using Section Formula.

`If \ the \ line \ segment \ AB \ where \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \ the \ points \ of \ P \ \\\\x = (ax_2 + bx_1)/(a+b) \ and \ y = (ay_2 + by_1)/(a+b)`

`Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b = 3 : 2\\\\Therefore, P (x, y) \\\\x = (3m + (2* -7))/(5) \ \ \ \ \ \ \ \ \ \ \ [ \ x = -1 \ ] \\\\-1 = (3m - 14)/(5)\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3`

`y =(3* 6 + 2 * 1)/(5)\\\\n = (18 + 2)/(5) = (20)/(5) = 4`