Lesson Split a line segment into n equal pieces

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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 {{{0 < m < n}}}
When I write xm, I really mean "x subscript m" or {{{x[m]}}}

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 {{{matrix(1,5,"(",x[m],",",y[m],")")}}} is {{{matrix(1,11,"(",x[m],",",y[m],")","=","(",a+expr(m/n)*abs(c-a),",",b+expr(m/n)*abs(d-b),")")}}}
where m is an integer such that {{{0 < m < n}}}
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.

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Further Reading:

An example where this formula is used
<a href = "https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1197813.html">https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1197813.html</a>

A similar lesson is shown here
<a href = "https://www.algebra.com/algebra/homework/Parallelograms/HOW-TO-divide-a-given-straight-segment-into-n-congruent-parts.lesson">https://www.algebra.com/algebra/homework/Parallelograms/HOW-TO-divide-a-given-straight-segment-into-n-congruent-parts.lesson</a> 
(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.