## Saturday, March 04, 2006

### Verbogeometry -- installment IV --- Midpoint Formula

2.3. Midpoint Formula in Verbogeometry: Any analytic geometry equation can use coordinate word-pairs instead of numbers to express poetic forms. Let us use the midpoint formula to express the exact point between the two points P1(praise,love) and P2(punishment,hate) from figure 13. Before we look at coordinate word-pairs let us refresh the use of the midpoint formula in analytic geometry. To find the midpoint between two points on a Cartesian coordinate system we add the x coordinates together and divide by 2 to find the x value for the midpoint and we also add the y coordinates together and divide by 2 to find the y value for the midpoint or
(x1 + x2)/2 = x0 and (y1 + y2)/2 = y0.
Lets look at an example of finding the midpoint P0 between the points P1(-14-15) and P2(12,11) utilizing the midpoint formula. x1 = -14 and x2 = 12 so substituting our numbers in the variables of the equation (x1 + x2)/2 = x0 we get (-14 + 12)/2 = -1 also y1 = -15 and y2 = 11 so substituting our numbers in the variables of the equation (y1 + y2)/2 = y0 we get (-15 + 11)/2 = -2 therefore: P0 = (-1,-2) (see figure 14.)

Figure 14.

Let us now take a different approach and replace the numeric variables in the midpoint equation with the words/concepts of love, hate, praise and punishment. We will use the form of coordinate word-pairs P2(love, praise) and P1(hate, punishment). The midpoint formula now shows us that P0(x0, y0) will be formed by the substitution of (x1 + x2)/2 = x0 with (love + hate) = x0 and (y1 + y2)/2 = y0 with (hate + punishment) = y0. Now we have expressed the exact point between love, praise and hate, punishment. (see figure 15.)

Here is a relative piece from 2000 http://www.kazmaslanka.com/midpoint.html