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Question
Find the ratio in which the point R ( 1, 5) divides the line segment joining the points S (-2, -1) and T (5, 13).
Solution
Let R divides the line segment ST in the ratio k : 1. Coordinates of R
R ( x, y) = R ( 1, 5)
R `((5"k" - 2)/("k" + 1) , (13 "k" - 1)/("k" + 1))` = R (1 , 5)
`(5"k" - 2)/("k" +1) = 1`
5 k - 2 = k + 1
4 k = 3
k = `3/4`
Hence, required ratiois k :1 = 3 : 4.
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