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| 1. |
(-3,10 ,)(6,-8) divided by -1,6 |
| Answer» Let A →\xa0(–3, 10), B → (6, –8) and P → (–1, 6)Let P divide AB in the ratio K: 1.{tex}P \\to \\left\\{ {\\frac{{(K)(6) + (1)( - 3)}}{{K + 1}},\\frac{{(K)( - 8) + (1)(10)}}{{K + 1}}} \\right\\}{/tex}or {tex}P \\to \\left( {\\frac{{6K - 3}}{{K + 1}},\\frac{{ - 8K + 10}}{{K + 1}}} \\right){/tex}But P {tex}\\rightarrow{/tex} (-1, 6){tex}\\therefore \\;\\frac{{6K - 3}}{{K + 1}} = - 1{/tex}{tex}\\Rightarrow{/tex} 6K - 3 = -K - 1{tex}\\Rightarrow{/tex} 7K = 2\xa0{tex}\\Rightarrow K = \\frac{2}{7}{/tex}and {tex}\\frac{{ - 8K + 10}}{{K + 1}} = 6{/tex}{tex}\\Rightarrow{/tex} -8k + 10 = 6K + 6{tex}\\Rightarrow{/tex} 14K = 4{tex}\\Rightarrow K = \\frac{4}{{14}} = \\frac{2}{7}{/tex} | |