Question

If the coordinator of the middle point of the portion of a line intercepted between the coordinate axes are (3, 2), then the equation of the line will be
(a) 2x + 3y = 12
(b) 3x + 2y = 12
(c) 4x – 3y = 6
(d) 5x – 2y = 10

Answer 1

Let us suppose points be A(a, 0) and B(0, b) an coordinate axis and (3, 2) is given to be the midpoint of AB

Hence, by midpoint formula,

$$\begin{gathered} \frac{a+0}{2}=3\mathrm{and}\frac{0+b}{2}=2 \\ \mathrm{i}.\mathrm{e}.a=6\mathrm{and}b=4 \\ \mathrm{Hence},\mathrm{equation}\mathrm{of}\mathrm{line}\mathrm{is}\frac{y-0}{x-a}=\frac{0-b}{a-0} \\ \mathrm{i}.\mathrm{e}.\frac{y}{x-6}=\frac{-4}{6} \\ \mathrm{i}.\mathrm{e}.3y=-2\left(x-6\right) \\ \mathrm{i}.\mathrm{e}.2x+3y=12 \end{gathered}$$

Hence, the correct answer is option A.