SchoolTutoring Submission Error - Please provide a valid contact phone number.
Close

Not a member yet? Register now and get started.

lock and key

Sign in to your account.

Account Login

Forgot your password?

Distance Between Two Parallel Lines

30 Nov Posted by in Geometry | Comments

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.