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Name: Robyn
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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.

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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