

Distance and Coordinate Formula
Name: Robyn
Status: student
Age: N/A
Location: N/A
Country: N/A
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
(xx1)^2+(yy0)^2=r^2, where r is the distance from the reference point to
the third point. Also, (yy0) must equal (slope)*(xx0). This translates
to (yy0)={(y1y0)/(xx0)}*(xx0). 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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Update: June 2012

