|
This Lesson (Split a line segment into n equal pieces) was created by by math_tutor2020(3817)
   : View Source, ShowAbout math_tutor2020: Middle school, high school, and college math tutor
Let (a,b) and (c,d) be the two endpoints of a segment. a,b,c,d are real numbers. Let's say we want to divide the segment into n equal pieces, where n is some positive integer such that n > 1. The goal therefore is to find the cutoff points. If n = 2, then use the midpoint formula and the rest of this lesson is a bit overkill. But let's say we wanted something like n = 4 instead. If so, then read on. The horizontal distance between the two points (a,b) and (c,d) is |c-a|. We subtract the x coordinates and apply absolute value to ensure the distance is never negative. Split that into n pieces to get (1/n)*|c-a| This represents the delta x value. delta = greek letter to represent change in value deltaX = (1/n)*|c-a| We'll add multiples of this deltaX value to the x coordinate of (a,b) xm = a + m*deltaX xm = a + m*(1/n)*|c-a| xm = a + (m/n)*|c-a| where m is an integer in the interval When I write xm, I really mean "x subscript m" or Similarly, deltaY = (1/n)*|d-b| ym = b + m*deltaY ym = b + m*(1/n)*|d-b| ym = b + (m/n)*|d-b| The location of the cutoff point where m is an integer such that This represents all of the n-1 cutoff points, so that the segment from (a,b) to (c,d) is split into n equal pieces. ------------------------------------------------------------------------------- Further Reading: An example where this formula is used https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1197813.html A similar lesson is shown here https://www.algebra.com/algebra/homework/Parallelograms/HOW-TO-divide-a-given-straight-segment-into-n-congruent-parts.lesson (credit goes to the tutor @ikleyn) in which the task of subdividing a line into n congruent pieces is done using a compass-and-straightedge approach. This current lesson uses coordinate geometry instead. It's always a good idea to know how both approaches work. This lesson has been accessed 932 times. |
