# Find the ratio m which on the x-axis divides the line segment joining the points (5,-6) and (1,-4)?

$we\;have\;two\;points\;A(1,-4),\;and\;B(5,-6)\\* Let\;suppose\;point\;C(x,0),\;which\;is\;on\;the\;x-axis\;is\;dividing\\* line\;joining\;A\;and\;B\;in\;the\;ratio\;m:n\\* \Rightarrow 0=\frac{-6m-4n}{m+n}\\* \Rightarrow 6m=-4n\\*\Rightarrow \frac{m}{n}=-\frac{2}{3}\\* \therefore point\;C(x,0)\;is\;dividing\;line\;joining\;A\;and\;B\;in\;the\;ratio\;2:3\;externally$

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