Question

Find the equation of the straight line perpendicular to the straight line $x-2y+3=0$ and passing through the point $(1,-2)$.

• A. $2x+y=0$
• B. $2x-y=0$
• C. $2x+y=3$
• D. None of these

Answer 1

Answer: (A)

$2x+y=0$

Consider the given equation.

$x-2y+3=0$ $...........\left(1\right)$

$slope{m}_1=\frac{1}{2}=$

Since, the line is perpendicular to given line. so slope $m_2$ will be

$m_1{m}_2=-1$

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

We know that the equation of the line which is passing through the point

$y-y_1=slope(x-x_1)$

So,

$y+2=-2(x-1)$

$y+2=-2x+2$

$2x+y=0$

Hence, this is the answer.