Find the ratio in which the joining of points $(-3,10)$ and $(6,-8)$ is divided by point $(-1,6)$.
Given :
$(-1,6)$ divides the line segment joining the points $(-3,10)$ and B$(6,-8)$.
To find :
We have to find the ratio of division.
Solution :
Let $(-1,6)$ divides $(-3,10)$ and $(6,-8)$ in the ratio $m:n$ internally.
The section formula is,
$(x, y) = (\frac{m x_{2} + n x_{1}}{m + n} , \frac{m y_{2} + n y_{1}}{m + n})$
Let $P(x, y) = P(-1, 6)$ ; $A (x_{1}, y_{1}) = A(-3, 10)$ ; $B(x_{2}, y_{2}) = B(6, -8)$
Therefore,
$(-1, 6) = (\frac{m (6) + n(-3)}{m + n} , \frac{m (-8) + n (-3)}{m + n} )$
On comparing,
$-1 = \frac{6m-3n}{m + n}$
$-1(m + n) = 6m-3n$
$-m-n = 6m-3n$
$6m+m-3n+n = 0$
$7m-2n = 0$
$7m = 2n$
$\frac{m}{n} = \frac{2}{7}$
$m : n = 2 : 7$
The required ratio is $2:7$.
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