In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8) ? Also, find the value of a.

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Solution

Let P (a, 6) divides the join of A(–4, 3) and B(2, 8) in the ratio k : 1.

$P space equals open parentheses fraction numerator 2 cross times k space plus space open parentheses negative 4 close parentheses cross times 1 over denominator space k plus 1 end fraction comma fraction numerator 8 cross times k space plus space 3 cross times 1 over denominator space k plus 1 end fraction close parentheses P space equals open parentheses fraction numerator 2 k space minus 4 over denominator space k plus 1 end fraction comma fraction numerator 8 k space plus space 3 over denominator space k plus 1 end fraction close parentheses fraction numerator 2 k space minus 4 over denominator space k plus 1 end fraction space equals m space a n d space space fraction numerator 8 k space plus space 3 over denominator space k plus 1 end fraction equals space 6 fraction numerator 8 k space plus space 3 over denominator space k plus 1 end fraction equals space 6 8 k space plus space 3 space equals space space 6 k plus 6 2 k space equals space 3 k space equals space 3 over 2$

ratio = 3:2

Now,
$fraction numerator 2 k space minus 4 over denominator space k plus 1 end fraction space equals m fraction numerator 2 cross times 3 over 2 space minus 4 over denominator space 3 over 2 plus 1 end fraction space equals m m space equals space minus 2 over 5$

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