Question

-10, -1)

What are the coordinates of the point on the directed line segment from
to (-3,-8) that partitions the segment into a ratio of 6 to 1?

Answer 1

9514 1404 393

Answer:

(-4, -7)

Explanation:

You seem to want P on AB such that ...

AP/PB = 6/1

AP = 6PB . . . . . . . . multiply by PB

P -A = 6(B -P) . . . . . show segment lengths as differences of point values

7P = 6B +A . . . . . . . rearrange

P = (6B +A)/7

We assume you want the directed segment AB such that A = (-10, -1) and B = (-3, -8). Then the point that does your partitioning is ...

P = (6(-3, -8) +(-10, -1))/7 = (-28, -49)/7

P = (-4, -7) . . . . the point that partitions the segment 6:1