Question

Find the distance of the line 4x+7y+5=0
from the point (1, 2) along the line 2x-y=0

Answer 1

We have to find the distance between point (1,2) and point of intersection lines

$4x+7y+5=0$ and $2x-y=0$

Now the pooint of intersection of lines $4x+7y+5=0$ and $2x-y=0$ is obtained by solving these equations.

$\therefore x=\frac{-5}{18}andy=\frac{-5}{9}$

$\therefore$ Distance between point (1,2) and

$(\frac{-5}{18},\frac{-5}{9})is\sqrt{(1+\frac{5}{18})+{(1+\frac{5}{9})}^2}$

$=\sqrt{{\left(\frac{23}{18}\right)}^2+{\left(\frac{23}{9}\right)}^2}$

$=\frac{23}{18}\sqrt{(1{)}^2+(2{)}^2}$

$=\frac{23}{18}\sqrt{5}$ units.