One end point of a line segment is (8,-1). The point (5,-2) is one third of the way from the endpoint to the other endpoint. Find the other endpoint.

Question

I have been having problems on this for my homework. Many have told me the answer is (-1,-4) but I just can't come to the conclusion on how they got that.

Answer 1

If the co-ordinates of the endpoints of a line segment are (a,b) and (c,d), then the point 1/3 of the way from (a,b) to (c,d) has co-ordinates: abscissa (2/3)a+(1/3)c and ordinate

(2/3)b+(1/3)d.

From this relationship you should be able to solve the problem...and the answer (1,-4) is correct.