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(C) Using the section formula for internal division,the coordinates of the point dividing the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in th

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$\left( \frac{19}{3}, \frac{8}{3} \right)$

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(C) Using the section formula for internal division,the coordinates of the point dividing the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m : n$ are given by $\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$.Here,$(x_1, y_1) = (4, -2)$,$(x_2, y_2) = (8, 6)$,$m = 7$,and $n = 5$.$x = \frac{7(8) + 5(4)}{7 + 5} = \frac{56 + 20}{12} = \frac{76}{12} = \frac{19}{3}$.$y = \frac{7(6) + 5(-2)}{7 + 5} = \frac{42 - 10}{12} = \frac{32}{12} = \frac{8}{3}$.Thus,the coordinates are $\left( \frac{19}{3}, \frac{8}{3} \right)$.

The coordinates of the point dividing internally the line segment joining the points $(4, -2)$ and $(8, 6)$ in the ratio $7 : 5$ are:

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