Question

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

Answer 1

Answer:

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Step-by-step explanation:

Let k : 1 be the ratio in which the point P ($\frac{3}{4},\frac{5}{12}$) divides the line segment joining the points A ($\frac{1}{2} ,\frac{3}{2}$) and B (2, -5). Then

$(\frac{3}{4}, \frac{5}{12} )=(\frac{k(2)+\frac{1}{2} }{k+1} , \frac{k(-5)+\frac{3}{2} }{k+1} )\\\\\implies \frac{k(2)+\frac{1}{2} }{k+1} = \frac{3}{4} \:\:and\:\: \frac{k(-5)+\frac{3}{2} }{k+1} = \frac{5}{12}\\\\\implies 8k + 2 = 3k+3\:\:and\:\:-60k+18=5k+5\\\\\implies k = \frac{1}{5} \:\:and\:\:k=\frac{1}{5}$

Hence, the required ratio is 1: 5.