Question

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!!!!​

Answer 1

Answer:

• P(1, 3)

Step-by-step 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

Answer 2

Answer: (1, 3)

Step-by-step 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.