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Question
If the line joining the points A(4, - 5) and B(4, 5) is divided by the point P such that `"AP"/"AB" = (2)/(5)`, find the coordinates of P.
Solution
From the given
`"AP"/"AB" = 2/5`
⇒ `"AP"/"AB" = 5/2`
`"AB"/"AP"-1 = 5/2-1`
⇒ `"PB"/"AP" = 3/2`
∴ coordinates of P
= `((mx_2+nx_1)/(m+x), (my_2+xy_1)/(m+x))`
= `((2xx4+3xx4)/(2+3), (2xx5+3xx(-5))/(2+3))`
= `((8+12)/5, (10-15)/5)`
= (4, -1)
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