Question

What are the coordinates of the point on the directed line segment from (1, -6) to (8, 8) that partitions the segment into a ratio of 4 to 3?

Answer 1

9514 1404 393

Answer:

  (5, 2)

Step-by-step explanation:

Line segment AB is partitioned by point P into segments of the ratio m : n when point P satisfies ...

  P = (mB +nA)/(m+n)

Here we want ...

  P = (4(8, 8) +3(1, -6))/(4 +3) = (32 +3, 32 -18)/7 = (35/7, 14/7)

  P = (5, 2)

The point (5, 2) partitions the segment into a ratio of 4 : 3.