Question

​Find the equation of the line through (2,3) so that the segment of the line intercepted between the axes is bisected at this point.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Equation}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{is}\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1\mathrm{which}\mathrm{meets}\mathrm{the}\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{axes}\mathrm{at}\mathrm{A}(\mathrm{a},0)\mathrm{and}\mathrm{B}(0,\mathrm{b})\mathrm{respectively}. \\ \mathrm{The}\mathrm{coordinates}\mathrm{of}\mathrm{the}\mathrm{mid}-\mathrm{point}\mathrm{of}\mathrm{AB}\mathrm{are}\left(\frac{\mathrm{a}}{2},\frac{\mathrm{b}}{2}\right). \\ \mathrm{Since}\mathrm{the}\mathrm{point}(2,3)\mathrm{bisects}\mathrm{AB},\mathrm{so}\frac{\mathrm{a}}{2}=2\mathrm{and}\frac{\mathrm{b}}{2}=3\Rightarrow \mathrm{a}=4\mathrm{and}\mathrm{b}=6. \\ \mathrm{Thus},\mathrm{Equation}\mathrm{of}\mathrm{the}\mathrm{staright}\mathrm{line}\mathrm{is}\frac{\mathrm{x}}{4}+\frac{\mathrm{y}}{6}=1\mathrm{or}3\mathrm{x}+2\mathrm{y}=12 \end{gathered}$$
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