Question

Find the ratio in which p(4,m)divide the line segment joiniing the points a(2,3)and b(6,-3).hence find m

Answer 1

Hi Mate !! 

A ( 2 , 3 )

P ( 4 , m )

B ( 6 , - 3 )

Let the point divides the AB in k : n ratio !! 

AP : PB = k : n 

• Using formula to find the x ( absissa ) of P 

x = ( x2 k+ x1 n )/k+ n

4 = ( 6k + 2n )/k + n

4k + 4n = 6k + 2n 

4k - 6k = 2n - 4n

- 2k = - 2n

k/n = -2/-2 

k/n = 1/1

k : n = 1 : 1

Since the point is dividing the line in 1 : 1 
hence , the point P is mid point of AB 

• Coordinate of P when P is mid point !! 

y = ( y1 + y2 )/2

y = ( 3 - 3 )/2

m = 0/2

m = 0

So, P ( 4 , 0 ) !!