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(D) If $P(x, y)$ divides the line segment joining $A(x_1, y_1)$ and $B(x_2, y_2)$ internally in the ratio $m: n$,then the coordinates are given by the

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$IV$ quadrant

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(D) If $P(x, y)$ divides the line segment joining $A(x_1, y_1)$ and $B(x_2, y_2)$ internally in the ratio $m: n$,then the coordinates are given by the section formula:$x = \frac{mx_2 + nx_1}{m + n}$ and $y = \frac{my_2 + ny_1}{m + n}$Given that $x_1 = 7, y_1 = -6, x_2 = 3, y_2 = 4, m = 1$ and $n = 2$.Substituting these values into the section formula:$x = \frac{1(3) + 2(7)}{1 + 2} = \frac{3 + 14}{3} = \frac{17}{3}$$y = \frac{1(4) + 2(-6)}{1 + 2} = \frac{4 - 12}{3} = -\frac{8}{3}$Thus,the point is $(\frac{17}{3}, -\frac{8}{3})$.Since the $x$-coordinate is positive and the $y$-coordinate is negative,the point lies in the $IV$ quadrant.

The point which divides the line segment joining the points $(7, -6)$ and $(3, 4)$ in the ratio $1: 2$ internally lies in the

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