Question

$A(1,3)$ and $B(7,5)$ are two opposite vertices of a square. The equation of a side through $A$ is

• A. $x+2y-7=0$
• B. $x-2y+5=0$
• C. $2x+y-5=0$
• D. None of these

Answer 1

The correct option is A $x+2y-7=0$

Let $m$ be slope of the line through A

Slope of $AB=\frac{5-3}{7-1}=\frac{1}{3}$

Joining $A$ and $B$, the angle between the side through $A$ and diagonal becomes ${45}^o$

We know that,

$\tan \theta =\left|\frac{m_1-m_2}{1+m_2{m}_2}\right|$

$\Rightarrow \tan {45}^o=\left|\frac{m-\frac{1}{3}}{1+\frac{m}{3}}\right|$

$\Rightarrow m=2$ or $-\frac{1}{2}$

Required equations are $x+2y-7=0$ or $2x-y+1=0$