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Name: Robyn
Status: student	
Age:  N/A
Location: N/A
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Date: N/A


Question:
Hi

I am tutoring an 11th grade student in geometry.

I have been trying to remember the formula for the coordinates of a point situated between two endpoints (the coordinates of the endpoints are known, as well as the distances between the unknown point and each endpoint).

I know it is similar to the midpoint formula, but the unknown point is NOT halfway between the endpoints. I would appreciate your help.



Replies:
Robyn, The formula is based on the Pythagorean Theorem, and the slope formula. If you know the distance from one point to the third point, then you know that (x-x1)^2+(y-y0)^2=r^2, where r is the distance from the reference point to the third point. Also, (y-y0) must equal (slope)*(x-x0). This translates to (y-y0)={(y1-y0)/(x-x0)}*(x-x0). In these equations, (x0,y0) and (x1,y1) are the end points. (x,y) is the third (unknown) point.

Ken Mellendorf
Illinois Central College
Physics Professor



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