Question

Point A is located at ​(4, 8)​ and point B is located at ​(14, 10)​ . What point partitions the directed line segment ​ AB¯¯¯¯¯ ​ into a 1:3 ratio?

(6 1/2, 8 1/2)
(11 1/2, 9 1/2)
 (6, 6)
 (9, 9)

Answer 1

A is the answer or (6 1/2, 8 1/2) or (13/2, 17/2) or (6.5,8.5)

Explanation:

Given : A line segment AB with

`A= (x_1,y_1)=(4,8)` and
`B= (x_2,y_2)=(14,10)`

let C partitioned the line AB by 1:3 let m:n = 1:3

shown in the figure attached

Formula used:

`C= ((n x_1 + m x_2 )/(m+n),(n y_1+ m y_2 )/(m+n))`

putting value in formula we get,

`C= (((4) (3)+ (14)(1) )/(1+3),((8)(3)+ (10)(1))/(1+3))`

`C= (((13 )/(2),(17)/(2))`

`C= (6.5 ,8.5)`

`C= ( 6 1/2,8 1/2)`

therefore, A is the answer