Question

The equation to the line bisecting the join of (3, –4) and (5, 2) and having its intercepts on the x-axis and the y-axis in the ratio 2 : 1 is.

• A. $x + y - 3 = 0$
• B. $2 x - y = 9$
• C. $x + 2 y = 2$
• D. $2 x + y = 7$

Answer 1

Answer: (C)

$x + 2 y = 2$

Answer 2

Given equation of line having it intercepts on the x- axis and y–axis in the ratio 2:1 i.e., 2a and a

∴ $\frac { x } { 2 a } + \frac { y } { a } = 1 \Rightarrow x + 2 y = 2 a$ .....(i)

According to question,

Line (i) also passes through midpoint of $( 3 , - 4 )$ and (5,2)

i.e., $( 4 , - 1 )$.

∴ $4 + 2 ( - 1 ) = 2 a \Rightarrow a = 1$

Hence the equation of required line is, $x + 2 y = 2$.