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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`.
Solution
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)`
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