255,161 views
45 votes
45 votes
Find the coordinates of point) along the directed segment AB that partitions it so that the ratio of AP to PB is 1:2. NO LINKS OR ASSESSMENT!!!!​

Find the coordinates of point) along the directed segment AB that partitions it so-example-1
User Oderfla
by
2.5k points

2 Answers

21 votes
21 votes

Answer: (1, 3)

Explanation:

There are two ways to solve this problem, 1 without the pythagorean theorem, and 1 with it. For the sake of simplicity, I will solve it without the pythagorean theorem.

As is visually evident from the graph, the line segment spans 6 units horizontally, and 3 units vertically. Because the ratio between AP and PB is 1:2, simply divide both the domain and range by 3, to get 2 horizontally, and 1 vertically.

Then, simply go to point A and respectively add and subtract the horizontal and vertical values to get point A(-1, 4) --> P(1,3)

Hope it helps, and let me know if you want me to solve it an alternate way or go more in depth as to the way it is know.

User Noco
by
3.3k points
22 votes
22 votes

Answer:

  • P(1, 3)

Explanation:

Coordinates of A and B:

  • A(-1, 4), B(5, 1)

The partition ratio:

  • AP/PB = 1/2

Coordinates of P are:

  • x = -1 + 1/3(5 - (-1)) = -1 + 6/3 = 1
  • y = 4 + 1/3(1 - 4) = 4 - 3/3 = 3
User Henry Crutcher
by
2.9k points