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

Explanation

Given lines, `4x+7y+5=0`……`(1)`
and `2x-y=0`…….`(2)`
Here, equation `(2)` passes through the point `A(1,2)`.
Solving equations `(1)` and `(2)`,
`x=(-5)/(18)` and `y=-(5)/(9)`
`:.` Point of intersection `B=((-5)/(18),(-5)/(9))`
Now, `AB=sqrt((1+(5)/(18))^(2)+(2+(5)/(9))^(2))`
`=sqrt((529)/(324)+(529)/(81))=sqrt((529)/(324)(1+4))`
`=(23sqrt(5))/(18)` unit.