Question

Peas help me
A point T on a segment with endpoints D(1, 4) and F(7, 1) partitions the segment in a 2:1 ratio. Find T. You must show all work to receive credit.

Answer 1

Hi ,

definition of section formula :

The point which divides internally  the line segment joining the points 

D( x1 , y1 ) and F ( x2 , y2 ) in the ratio m : n  is 
 
T ( mx2 + nx1 / m+n , my2 + ny2 / m+n ) 


According to the problem ,

D( x1 , y1 ) = ( 1 , 4 ) 

F ( x2 , y2 ) = ( 7 , 1 )

ratio = m: n = 2 :1


let  T =  ( x , y ) 


x = (mx2 + nx1 ) / ( m+n ) 

   = ( 2 × 7 + 1 × 1 ) / ( 2+1 )

   = (14 +1 ) / 3

   = 15 /3 

 x = 5

y = ( my2 + ny1) /(m+n )

   = ( 2 × 1  + 1 × 4 ) / ( 2+ 1 )

   = (2 + 4) / 3

   = 6/ 3

y = 2

therefore,

T ( x , y ) = ( 5 , 2 )

i hope this is helps you .

*****