What are the coordinates of the point on the directed line segment from ( − 4 , 5 ) (−4,5) to ( − 1 , − 7 ) (−1,−7) that partitions the segment into a ratio of 2 to 1?

Answer 1

If I assume you mean to divide the line segment with endpoints (-4,5) and (-1,-7), there are 2 answers depending on which segment is to be the longer.

One set of co-ordinates is (-3,1).

You can certainly, in this case, get the answer graphically by plotting the 2 points.

You can also derive this answer or a general answer using algebra and the graph of a straight line.

You will need the so-called "Side Splitter" Theorem.