Find the ratio in which the point P(3/4 , 5/12) divides the line segment joining points A(1/2 , 3/2) and B(2,-5) .

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Solution

Dear Student,

$l e t t h e r a t i o i n w h i c h p o i n t P d i v i d e s b e k : 1 c o o r d i n a t e s o f P = \frac{\frac{1}{2} + 2 k}{k + 1} = \frac{1 + 4 k}{2 k + 2}, \frac{\frac{3}{2} - 5 k}{k + 1} = \frac{3 - 10 k}{2 k + 2} b u t P i s (\frac{3}{4}, \frac{5}{12}) s o, \frac{1 + 4 k}{3 - 10 k} = \frac{3}{4} \times \frac{12}{5} = \frac{9}{5} 5 + 20 k = 27 - 90 k \Rightarrow 110 k = 22 \Rightarrow k = 1 : 5$
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