Question

The opposite vertices of a square are $\left(1,2\right)$ and $\left(3,8\right)$, then the equation of a diagonal of the square passing through the point $\left(1,2\right)$, is

• A. $3x-y-1=0$
• B. $3y-x-1=0$
• C. $3x+y+1=0$
• D. None of these

Answer 1

The correct option is A

$3x-y-1=0$

Step 1: Find the slope of the straight line

Let the opposite vertex of the square are $A\left(1,2\right)$ and $B\left(3,8\right)$

$AB$ is diagonal

Therefore slope of $AB$, $m=\frac{y_2-y_1}{x_2-x_1}$

$$\begin{gathered} =\frac{8-2}{3-2} \\ =\frac{6}{2} \\ =3 \end{gathered}$$

Step 2: Find the equation of the straight line

The equation of the line passing through $\left(1,2\right)$ is

$$\begin{gathered} \mathbf{}\mathbf{}\mathit{y}\mathbf{-}{\mathit{y}}_{\mathbf{1}}\mathbf{=}\mathit{m}\left(x-x_1\right) \\ \Rightarrow y-2=3\left(x-1\right) \\ \Rightarrow 3x-y-1=0 \end{gathered}$$

Hence, the correct option is $\left(\mathrm{A}\right)$.