Question

Find the point, M, that divides segment AB into a ratio of 2:1 if A is at (-1, 2) and B is at (8, 15). A) (6, 8) B) (6, 26 3 ) C) (5, 32 3 ) D) (5, 26 3 ) 27)

Answer 1

Hence, the coordinate of point M that divides the line segment AB is
`(5, (32)/(3) )`.

Explanation:

Given that,

AB is the line segment, and M divides the line segment AB into a ratio of 2:1.

Coordinate of point A is
`(-1, 2)` and Coordinate of point B is
`(8, 15)`.

Let, the coordinate of point M is
`(x. y)`.

Now,

The coordinate of a point M, which divides the line segment AB internally in the ratio
`m_(1):m_(2)` are given by:

`(m_(1)x_(2)+m_(2)x_(1) )/((m_(1)+m_(2)) ) ,(m_(1)y_(2)+m_(2)y_(1) )/((m_(1)+m_(2)) )`

`x` coordinate of point M is
`((2* 8)+(1* -1))/((2+1))` =
`((16-1))/(3) =(15)/(3) =5`

`y` coordinate of point M is
`((2* 15)+(1* 2))/((2+1))` =
`(30+2)/(3) = (32)/(3)`

Hence, the coordinate of point M that divides the line segment AB is
`(5, (32)/(3) )`.