Question

"find the coordinates of the foot of the perpendicular drawn from the point (1 -2) to the line y=2x+1"

Answer 1

Answer:

$\text{The foot of the perpendicular is (-1,-1)}$

Step-by-step explanation:

$\text{The foot of perpendicular from the point ( 1, -2) to the line 2x-y+1=0 is given by }$

$\boxed{\bf\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{-(ax_1+by_1+c)}{a^2+b^2}}$

$\text{Here, }$

$(x_1,y_1)=(1,-2)$

$a=2,\,b=-1,\,c=1$

$\frac{x-1}{2}=\frac{y+2}{-1}=\frac{-(2(1)-1(-2)+1)}{2^2+(-1)^2}$

$\frac{x-1}{2}=\frac{y+2}{-1}=\frac{-(2+2+1)}{4+1}$

$\frac{x-1}{2}=\frac{y+2}{-1}=\frac{-5}{5}$

$\frac{x-1}{2}=\frac{y+2}{-1}=-1$

$\implies$

$\frac{x-1}{2}=-1$

$x-1=-2$

$x=1-2$

$x=-1$

$\implies$

$\frac{y+2}{-1}=-1$

$y+2=1$

$y=1-2$

$y=-1$

$\therefore\textbf{The foot of the perpendicular is (-1,-1)}$

Answer 2

Answer:

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