Question

Find the ratio in wch the line segment joining the points (-3,10) and (6,-8) is divided by (-1,6). Please answer it fast.

Answer 1

refer to the attachment

Answer 2

$Let \: the \: ratio \:of \: the \:line \: segment \\joining \: the \: points \: A(-3,10) = (x_{1}, y_{1}) \\and \: B(6,-8) = ( x_{2}, y_{2})\: is \: divided \: by \\P(-1,6)) \\is \: k : 1$

$\underline {\blue { By \:Section \: Formula : }}$

$\Big( \frac{kx_{2} + x_{1}}{k+1} , \frac{ky_{2} + y_{1}}{k+1}\Big) = ( -1 , 6 )$

$\implies \Big( \frac{k \times 6 + (-3)}{k+1}, \frak{k \times (-8) + 10}{k+1}\Big) = ( -1 , 6 )$

$\implies \Big( \frac{6k-3}{k+1} , \frac{-8k+10}{k+1}\Big) = ( - 1,6 )$

/* Take first coordinates in both sides */

$\implies \frac{6k-3}{k+1} = -1$

$\implies 6k-3 = -(k+1)$

$\implies 6k-3 +(k+1) = 0$

$\implies 6k + k -3 + 1 = 0$

$\implies 7k = 2$

$\implies k = \frac{2}{7}$

$\implies k : 1 = 2 : 7$

Therefore.,

$\red { Required \: ratio } \green { = 2 : 7 }$

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