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(A) Let the ratio in which the line segment joining the points $A(-3, 10)$ and $B(6, -8)$ is divided by the point $P(-1, 6)$ be $k : 1$.Using the sect

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$2$:$7$

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(A) Let the ratio in which the line segment joining the points $A(-3, 10)$ and $B(6, -8)$ is divided by the point $P(-1, 6)$ be $k : 1$.Using the section formula,the coordinates of point $P$ are given by:$P(x, y) = \left( \frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n} \right)$Here,$m = k$,$n = 1$,$(x_1, y_1) = (-3, 10)$,and $(x_2, y_2) = (6, -8)$.Equating the $x$-coordinate:$-1 = \frac{k(6) + 1(-3)}{k + 1}$$-1(k + 1) = 6k - 3$$-k - 1 = 6k - 3$$-k - 6k = -3 + 1$$-7k = -2$$k = \frac{2}{7}$Thus,the required ratio is $2 : 7$.

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

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