First slide

Equation of line in Straight lines

Question

If the segment of the line between the lines $x - y + 2 = 0$ and $x + y + 4 = 0$ is bisected at the origin, equation of the line is

Moderate

A

$y + 3 x = 0$
B

$x + 3 y = 0$
C

$y - 3 x = 0$
D

$x - 3 y = 0$

Solution

Let the required line meet the given lines at $(α_{1}, β_{1})$ and $(α_{2}, β_{2})$ respectively.
then $α_{1} - β_{1}, + 2 = 0, α_{2} + β_{2} + 4 = 0$
Also $\frac{α_{1} + α_{2}}{2} = 0, \frac{β_{1} + β_{2}}{2} = 0$
$\Rightarrow α_{2} = - 1, β_{2} = - 3$ and $α_{1} = 1, β_{1} = 3$
Equation of the line passing through $(1, 3)$ and $(0, 0)$ is
$y = 3 x \Rightarrow y - 3 x = 0$

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