Question

Find the coordinates of the foot of the perpendicular drawn from the point (1,-2) on the line y=2x+1.

Answer 1

Since $2$ lines are $\perp$, then product of slope $=-1$

$i_1:y=2x+1$

or $y-2x=1$

or $y-2x=1---\left(1\right)$

$m_1=1$

Let the foot be or $D(x_1,x{y}_1)$

Since product of slope $=-1$

$m_2=-1$

$(1,-2)$

$(y_1+2)=-1(x,-1)[\because (y_1-y_{)}2)=m_2(x_1-x_2\left)\right]$

$y_1+2=-x_1+1$

$y_1+x_1=-1$

or $y+x=-1$

Solving $\left(1\right)$ & $\left(2\right)$

$y-2x=1$

$y+x=1$

Subtracting both reacts in

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

$3x=-2$ or $(x=\frac{-2}{3})$

$y=1+2x=1+2\times \frac{-2}{3}=(\frac{-1}{3}=y)$

or

coordinate of foot: $(\frac{-2}{3},\frac{-1}{3})$