Distance Between Two Parallel Lines

We know that the perpendicular distance from origin to a straight line whose equation is a+by+c=0 is |c|/√(a²+b²). Also, we know that the perpendicular distance from (h,k) to ax+by+c=0 is, |ah+bk+c|/√(a²+b²). These two are the formulas to find out the distances to a line from origin or a point. But, how to find the distances between two parallel lines? Let us derive the formula for the distance between two parallel lines.

The general form of equation of a straight line is ax+by+c=0 whose slope is –a/b.

We know the fact that any two lines are parallel if they have same slope. Thus, any two parallel lines have same coefficients of x and y but differs in constants.

Let ax+by + p =0 and ax+by + q =0 be two parallel lines and let us find the distance between these lines now.

Let (h,k) be a point of the line ax+by+p=0

Then ah+bk +p=0 à ah+bk =-p …(1)

Now distance from (h,k) to the second line ax+by +q=0 according to formula is,

|ah+bk+q|/√(a²+b²)

=|-p+q |/√(a²+b²) (By using equation (1))

=|p-q |/√(a²+b²)

Thanks for reading this Mathematics tutorial and remember we can help you with your French tutoring.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Saskatchewan visit: Tutoring in Saskatchewan.