Question

A straight line through P(1, 2) is such that its intercept between the axes is bisected at P. Its equation is.

• A. $x + 2 y = 5$
• B. $x - y + 1 = 0$
• C. $x + y - 3 = 0$
• D. $2 x + y - 4 = 0$

Answer 1

Answer: (D)

$2 x + y - 4 = 0$

Answer 2

Let the equation of the line be $\frac { x } { a } + \frac { y } { b } = 1$ . The coordinates of the mid point of the intercept AB between the axes are $\left( \frac { a } { 2 } , \frac { b } { 2 } \right)$.

∴ $\frac { a } { 2 } = 1 , \frac { b } { 2 } = 2 \Rightarrow a = 2 , b = 4$.

Hence the equation of the line is $\frac { x } { 2 } + \frac { y } { 4 } = 1$ , $2 x + y = 4$