Prove that the line passing through the points `(x_(1),y_(1))` and `(x_(2),y_(2))` is at a distance of `|(x_(1)y_(2)-x_(2)y_(1))/(sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)))|` from origin.

Explanation

Equation of a line passing through the points `(x_(1),y_(1))` and `(x_(2),y_(2))`
`y-y_(1)=(y_(2)-y_(1))/(x_(2)-x_(1))(x-x_(1))`
`implies y(x_(2)--x_(1))-y_(1)x_(2)+-x_(1)y_(1)=x(y_(2)-y_(1))-x_(1)y_(2)+x_(1)y_(1)`
`implies x(y_(2)-y_(1))-y(x_(2)-x_(1))-x_(1)y_(2)+x_(2)y_(1)=0`
Length of perpendicular from `(0,0)`
`=|(0-0-x_(1)y_(2)+x_(2)y_(1))/(sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)))|`
`=|(x_(1)y_(2)-x_(2)y_(1))/(sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)))|`