Reduce the lines `3x-4y+4=0` and `4x-3y+12=0` to the normal form and hence determine which line is nearer to the origin.

Explanation

`3x-4y+4=0`

`implies -3x+4y=4`

`implies-frac{3}{sqrt{(-3)^2+4^2}}x4/sqrt{(-3)^2+4^2}y=4/sqrt{(-3)^2+4^2}`

`implies -3/5x+4/5y=4/5ldots`(i)

Now, `4x-3y+12=0`

`implies -4x+3y=12`

`implies -4/sqrt{4^2+3^2}+3/sqrt{4^2+3^2}=12/sqrt{4^2+3^2}`

`implies -4/5+3/5=12/5ldots`(ii)

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