Question

What are the coordinates of the point on the directed line segment from (−6,8) to (6,−7) that partitions the segment into a ratio of 2 to 1?

Answer 1

Answer:

  (2, -2)

Step-by-step explanation:

The difference of coordinates is ...

  (6, -7) -(-6, 8) = (12, -15)

The point of interest is located 2/(2+1) = 2/3 of this distance from the first point. So, the point of interest is ...

  first point + 2/3 distance

  = (-6, 8) + (2/3)(12, -15)

  = (-6, 8) + (8, -10)

  = (2, -2)

_____

In symbolic terms, the point P that is 2/3 of the distance from A to B is ...

  P = A + (2/3)(B -A) = (1/3)A +(2/3)B

  P = (A +2B)/3

Filling in the coordinate values, we find ...

  P = ((-6, 8) +2(6, -7))/3 = (-6+12, 8-14)/3 = (6, -6)/3

  P = (2, -2)