Ratios and directed line segments

Question

What are the coordinates of the point on the directed line segment from (−10,2) to (−10,−5) that partitions the segment into a ratio of 6 to 1?

Answer 1

A ratio of 6 to 1 means that the first part of the line will have length 6/7 * (total length) and the second one will have length 1/7 * (total length).

Here the total length is 7, so the line starting at (-10,2) will have length (6/7)*7, or 6. The x coordinates of the start and end points are the same, so the point on the line will also have x = -10, which means that to find the point, all we have to do is go 6 along the line, which in this case means subtracting 6 from the starting y coordinate: 2.

In the end, this gives us the point (-10,-4).