Question

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

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

Answer 1

Answer: (A)

Given line $x-2y+3=0$ can be written as
$y=\frac{1}{2}x+\frac{3}{2}\dots \left(i\right)$
Slope of the line $\left(i\right)$ is $m_1=\frac{1}{2}$. Therefore, slope of the line perpendicular to line $\left(i\right)$ is
$m_2=-\frac{1}{m_1}=-2$
$\therefore$ Equation of the line with slope $-2$ and passing through the point $\left(1,-2\right)$ is
$y-\left(-2\right)=-2\left(x-1\right)$ or $y=-2x$