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

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The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the IV quadrant. Explanation: If P(x, y) divides the line segment joining A(x1, y2) and B(x2, y2) internally in the ratio m : n, Then x = (mx_2 + nx_1)/(m + n) and y = (my_2 + ny_1)/(m + n) Given that, x1 = 7, y1 = – 6, x2 = 3, y2 = 4, m = 1 and n = 2 $\therefore$ x = (1(3) + 2(7))/(1 + 2), y = (1(4) + 2(-6))/(1 + 2) ...[By section formula] $\Rightarrow$ x = (3 + 14)/3, y = (4 - 12)/3 $\Rightarrow$ x = $\frac{17}{3}$, y = -$\frac{8}{3}$ So, (x, y) = ($\frac{17}{3}$, -$\frac{8}{3}$) lies in IV quadrant. ...[Since, in quadrant, x-coordinate is positive and y-coordinate is negative]

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