What are the coordinates of the point on the directed line segment from (-10, -3) to (-3, -3) that partitions the segment into a ratio of 3 to 4?

9514 1404 393

  (-7, -3)

Step-by-step explanation:

The point is the weighted sum of the end point coordinates. The weights are the reverse of the adjacent segment proportions.

  P = (4(-10, -3) +3(-3, -3))/7 = (-40-9, -12-9)/7 = (-49, -21)/7

  P = (-7, -3)

The point that partitions the segment in the desired fashion is (-7, -3).

Alternate solution

The given segment can be recognized as a horizontal segment of length 7. Then the desired point is 3 units from the first end, so at (-10+3, -3) = (-7, -3).