Question

Segment AB has endpoints at A  4, 8 and B10,13 . If point P lies on AB such that AP BP : 2 : 5  , then find the coordinates of P. Show all your work.

Answer 1

Hence, the coordinate of point P is
`((40)/(7), (66)/(7))`.

Explanation:

Given that,

AB is the line segment having endpoints are A and B.

Coordinate of point A is
`(4, 8)` and coordinate of point B is
`(10, 13)`.

Point P lies on line segment AB which divides the line segment AB in the 2:5.

Let, the coordinate of point P which divides the line segment AB is
`(x, y)`.

Now,

The coordinate of a point P, 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 P is
`(2* 10+5* 4)/(2+5) =(20+20)/(7)=(40)/(7)`

`y` coordinate of point P is
`(2* 13+5* 8)/(2+5) =(26+40)/(7) =(66)/(7)`

Hence, the coordinate of point P is
`((40)/(7), (66)/(7))`.