Question

A line passes through the point P (1, 2) such that its intercept between the axes is bisected at P. The equation of the line is
(a) x + 2y = 5
(b) x – y + 1 = 0
(C) x + y – 3 = 0
(d) 2x + 2y – 4 = 0

Answer 1

Suppose equation of the line is given by $\frac{x}{a}+\frac{y}{b}=1$

Since intercept between is axis is bisected


$$\begin{gathered} \frac{a+0}{2}=1\mathrm{and}\frac{0+b}{2}=2\left(\mathrm{By}\mathrm{mid}\mathrm{point}\mathrm{formula}\right) \\ \mathrm{i}.\mathrm{e}.a=2\mathrm{and}b=4 \\ \therefore \mathrm{equation}\mathrm{of}\mathrm{line}\mathrm{is}\frac{x}{2}+\frac{y}{4}=1 \\ \mathrm{i}.\mathrm{e}.2x+y=4 \\ \mathrm{i}.\mathrm{e}.2x+y-4=0 \end{gathered}$$

Hence, the correct answer is option D.