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| 1. |
FIND THE RATIO IN WHICH LINE SEGMENT JOINING A(1,-5),(-4,5) IS DIVIDED BY THE xAxis |
| Answer» Let the point of division be P. Let the ratio be K : 1.Then{tex} P \\to \\left\\{ {\\frac{{(K)( - 4) + (1)(1)}}{{K + 1}},\\frac{{(K)(5) + (1)( - 5)}}{{K + 1}}} \\right\\}{/tex}{tex}P \\to \\left\\{ {\\frac{{ - 4K + 1}}{{K + 1}},\\frac{{5K - 5}}{{K + 1}}} \\right\\}{/tex}{tex}\\because{/tex} P lies on the x-axis and we know that on the x-axis the ordinate is 0.{tex}\\therefore \\;\\frac{{5K - 5}}{{K + 1}} = 0{/tex}{tex}\\Rightarrow{/tex} 5K - 5 = 0{tex}\\Rightarrow{/tex} 5K = 5{tex}\\Rightarrow K = \\frac{5}{5} = 1{/tex}Hence, the required ratio is 1 : 1.Putting K = 1, we get{tex}P \\to \\left\\{ {\\frac{{ - 4(1) + 1}}{{1 + 1}},\\frac{{5(1) - 5}}{{1 + 1}}} \\right\\}{/tex}{tex}P \\to \\left\\{ { - \\frac{3}{2},0} \\right\\}{/tex} | |