[futurebasic] Re: Coordinate geometry.

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From: Brian Victor <bhv11@...>
Date: Thu, 11 Dec 1997 20:27:08 -0500
At 9:08 AM -0500 12/11/97, Chris wrote:
>>Does anyone know the answer to these two geometry questions?
>>
>>1. The formula for finding the intersection point of two lines.
>The intersection point of two lines is found by setting the two line
>equations equal to each other, solving for x and then substituting that
>value into one of the original equations to find y.

That's exactly the concept.  Getting it into BASIC is just a matter of
reducing it to two equality statements.  For the moment, I'll assume that
your linear equations are in slope-intercept form.  (y=mx+b)  If they're
not, you'll have to add a step to get them there.  For each equation, you
have two coefficients, and therefore two variables.

y1 = ax + b
y2 = cx + d

a, b, c, and d are your variables.  Through algebra we can solve for x in a
form that will work nicely for an assignment statement.

 ax + b = cx + d
ax - cx = d - b
 (a-c)x = d - b
      x = (d-b)/(a-c)

That last line will plug right into BASIC, with changes allowed for your
own particular variable names.  Note however that it would be prudent to
make your x and y variables either single or double precision variables
(append either a # or a ! to the variable name: x# or x!) in order to allow
for the decimals that you're likely to run into.  To locate the y
coordinate, take one of your original equations and plug in your x value,
which you now know:

y = a * x + b

This should solve your first problem for you.  The second will be more of a
challenge.  I'll look it over and see what I can come up with.

-- Brian Victor