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(-3,10 ,)(6,-8) divided by -1,6

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(-3,10 ,)(6,-8) divided by -1,6

Posted by Parth Manwatkar 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Let A → (–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
{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}

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