Question

What are the coordinates of the point on the directed line segment from (-8,2) to (7,-3) that partitions the segment into a ratio of 3 to 2?

Answer 1

Answer:

  (1, -1)

Step-by-step explanation:

One way to find the point is this.

The point P that divides AB into segments AP/PB = 3/2 can be found to be ...

  P = A +(AP/AB)(B -A)

  P = (-8, 2) + (3/5)(7-(-8), -3-2)

  P = (-8, 2) +3/5(15, -5) = (-8, 2) +(9, -3) = (-8+9, 2-3)

  P = (1, -1)

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Another way to find the point is ...

  AP/PB = 3/2

  2(P -A) = 3(B -P)

  5P = 3B +2A

  P = (3B +2A)/5 = (3(7, -3) +2(-8, 2))/5 = (21 -16, -9 +4)/5 = (5, -5)/5

  P = (1, -1)