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Section Ratio


Given the points THE(xTHE, yTHE), B(xB, yB), Ç(xÇ, yÇ) of the same line , point C divides for a certain reason, called section ratio and indicated by:

on what because if , then A = B.

Note the following representation:

As the , we can write:

Let's look at some examples:

  • Considering the points THE(2, 3), B(5, 6) and P(3, 4), the reason why the point P divide é:


If we calculated rP Using the ordinates of the points, we would get the same result:

  • To the points THE(2, 3), B(5, 6) and P(1, 2) we have:

So for one point P any relative to a segment oriented contained in an axis, we have:

  • if P is inside a , then rP > 0

  • if P is outside of , then rP < 0

  • if P = A, then rP =0

  • if P = B, then there is no rP (PB = 0)

  • if P is the midpoint of , then rP =1

Nearby: Midpoint