The straight line passing through $(0,0)$ and the foot of perpendicular from $(2,4)$ onto $\dot{x}+y-1=0$

Question

Aicharya · Accepted Answer

$\frac{h-2}{1}=\frac{k-4}{1}=-\frac{(2+4-1)}{1^2+1^2}$ $\begin{aligned} & \Rightarrow \quad h=2-\frac{5}{2} \text { and } k=4-\frac{5}{2} \\ & \Rightarrow \quad h=-\frac{1}{2} \text { and } k=\frac{3}{2}\end{aligned}$

$\therefore$ Equation of line passing through $(0,0)$ and $\left(-\frac{1}{2}, \frac{3}{2}\right)$ $\Rightarrow y=\left(\frac{\frac{3}{2}-0}{-\frac{1}{2}-0}\right) x$, i.e. $y=-3 x$

The straight line passing through $(0,0)$ and the foot of perpendicular from $(2,4)$ onto $\dot{x}+y-1=0$

Solution