Question

Find the coordinates of a point P, which lies on the line segment joining the points A (−2, −2), and B (2, −4), such that `AP=3/7 AB`.

Answer 1

It is given that,`AP=3/7 AB`. where A, P and B are three points on line segment AB.

`rArr(AB)/(AP)=7/3`

`rArr(AB)/(AP)=-1=7/3-1`

`rArr(AB-AP)/(AP)=(7-3)/3`

`rArr (PB)/(AP)=4/3`

Thus, AP : PB = 3 : 4

It is given that, the coordinates of points A and B are (−2, −2) and (2, −4).

Using section formula,

Coordinates P are `((3xx2+4xx(-2))/(3+4),(3xx(-4)+4xx(-2))/(3+4))`

`=((6-8)/7,(-12-8)/7)=(-2/7,-20/7)`

Hence, the coordinates of point P are`(-2/7,-20/7)`