First slide

Equation of line in Straight lines

Question

If $x + 2 y + 3 = 0, x + 2 y - 7 = 0$ and $2 x - y - 4 =$ 0 form three sides of a square, the equation of the fourth side nearer the point (1, - 1) is

Easy

A

$2 x - y - 6 = 0$
B

$2 x - y + 6 = 0$
C

$2 x - y - 14 = 0$
D

$2 x - y + 14 = 0$

Solution

Equation of the fourth side is $2 x - y - k = 0$
such that $\frac{4 - k}{\sqrt{5}} = \pm \frac{3 + 7}{\sqrt{5}} \Rightarrow k = - 6 or 14$
So the required equation is $2 x - y + 6 = 0$ , it is
nearer to (1, –1).

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