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Find the ratio in which the line segment joining the points (-3, 10) and (6, – 8) is divided by (-1, 6).
Answer :

Let the required ratio be k : 1
By section formula ,

\( x = \frac{m1x2 + m2x1}{m1+m2} \)
\( \Rightarrow -1 = \frac{k×6 + 1× -3 )}{k+1} \)
\( \Rightarrow -k-1 = 6k -3 \)
\( \Rightarrow 7k = 2 \)
\( \Rightarrow k = \frac{2}{7} \)

The required ratio = k : 1
= \(\frac{2}{7} \) : 1 = \(\frac{2}{7} ×7 : 1×7 \) = 2 : 7

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