Question

What are the coordinates of the point on the directed line segment from (-4,-9) to (2, 3) that partitions the segment into a ratio of 1 to 3?

Answer 1

From (-4,-9) to (1,1), Δx = 5 and Δy = 10. If we divide the line into 5 equal pieces, each piece is increased by Δx = 1 and Δy = 2 from the previous point. After 3 pieces, the coordinates are (-4+3,-9+6) which is 3/5 of the total length with 2/5 remaining. Therefore the point (-1,-3) partitions the line into two segments with length ratio 3:2.