Question

find the ratio in which p(4m) divides the line segment joining the point A(2,3)and B(6,-3) hence find m

Answer 1

Let P (4,m) divide the join of A(2,3) and B(6,-3) in the ratio k:1
 P(4,m)  = [( 6k +2)/(k+1), (-3k+3)/(k+1)]
(6k+2)/(k+1)=4
6k+2=4k+4    (cross multiplication)
2k=2
k=1
Therefore, P(4,m) divides AB in the ratio 1:1. 
m= -3+3/2 = 0

Answer 2

Given: P(4, m) , point A(2,3)and B(6,-3)

To find: ratio, m

Solution:

• As we have given that, P divides line segment AB in a certain ratio,

• So, let the ratio be n:1.

• So, now using segment formula,

            (mx2 + nx1) / (m+n) , (my2 + ny1) / (m+n)

• Putting values in the formula, we get:

           P(4,m)  = ( 6n +2) / (n+1), (-3n+3) / (n+1)

• Solving the equation further, we get:

           (6n+2) / (n+1) = 4

           6n + 2 = 4n + 4    

           2n = 2

           n = 1

Answer:

•   So, therefore, P(4,m) divides AB in the ratio 1:1. 

            m= -3+3/2 = 0