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

Explanation

Let `4x+7y+5=0\ldots(i)`

and `2x-y=0ldots(ii)`

Putting `y=2x` from `(ii)` in `(i),` we get `4x+7(2x)+5=0`

`\implies x=frac{-5}{18}`

and `y=frac{-5}{9}`

`\implies `The intersecting point of given two lines is `(frac{-5}{18},frac{-5}{9})`

So, the required distance is the distance between the intersecting point and the given point, i.e.

`sqrt{(1+frac{5}{18})^2+(2+frac{5}{9})^2}`

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