Question

A vertex of square is $(3,4)$ and diagonal's equation is given by $x+2y=1$,then the second diagonal which passes through given vertex will be

• A. $2x-y+2=0$
• B. $x+2y=11$
• C. $2x-y=2$
• D. None of these

Answer 1

Answer: (C)

$2x-y=2$

Diagonals of Square are perpendicular bisector of each other.

$x+2y=1\Rightarrow y=\frac{-x}{2}+\frac{1}{2}$
Comparing with $y=mx+c$ we have $slope=m_1=\frac{-1}{2}$

As diagonals are perpendicular, so

$m_1\times m_2=-1$

$\frac{-1}{2}\times m_2=-1$

$m_2=2$

equation of other diagonal is $y=2x+c$

as this passes through $(3,4)$ it satifies the equation

$\Rightarrow 4=2\left(3\right)+c\Rightarrow c=-2$

Thus equation of diagonal $\equiv 2x-y-2=0$
Hence, the answer is option $C$