Question

If (2,-3) is the foot of the perpendicular from (-4,5) on a line then its equation is

• A. 3x-4y+28=0
• B. 3x-4y-18 =0
• C. 3x-4y+18=0
• D. 3y-4y+12=0

Answer 1

The correct option is B 3x-4y-18 =0

We are going to find slope of $AB$

$m_{AB}=\frac{5-(-3)}{-4-2}$

$\Rightarrow$ $m_{AB}=\frac{8}{-6}$

$\therefore$ $m_{AB}=\frac{-4}{3}$

Now,

$m_L\times m_{AB}=-1$

$\Rightarrow$ $m_L\times \left(\frac{-4}{3}\right)=-1$

$\Rightarrow$ $m_L=\frac{3}{4}$

The required equation,

$\Rightarrow$ $y-y_1=m_L(x-x_1)$

$\Rightarrow$ $y-(-3)=\frac{3}{4}(x-2)$

$\Rightarrow$ $4(y+3)=3x-6$

$\Rightarrow$ $4y+12=3x-6=0$

$\Rightarrow$ $3x-4y-18=0$