March 29, 2015

Homework Help: Finding a Formula, help please !

Posted by Paris on Sunday, January 14, 2007 at 7:08pm.

Does anyone know the formula to find any point between two other given points in a line?

Please, and thank you!

The mindpoint formula

xm= _(x1 + x2) /2

ym = (y1 + y2) /2

This give the midpoint (xm, ym) between the points x1,y1 and x2,y2

Thanks for the tip, but I was wondering if there's a formula for any point, not just the midpoint...

Thank you again!

Let P(x,y) be a point between A(x1,y1) and B(x2,y2) so that AP:PB = m:n then

P(x,y)= ((n*(x1,y1) + m*(x2,y2))/(m+n) in vector terminology or

x = ((n*x1 + m*x2))/(m+n)
y = ((n*y1 + m*y2))/(m+n)

hope this helps

Test it with A(7,14) and B(14,21) in the ratio of 5:2

then P is (12,19) and
AP = 5root2 and PB=2roots2 which is 5:2

oh, thank you!

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