2. given a directed line segment with endpoints a(3, 2) and b(6, 11), what is the point that
divides ab two-thirds from a to b?

The point of division is (5 , 8)

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divides the line whose endpoints are

 and at ratio , then

  and

* Lets solve the problem

- The directed line segment with endpoints A (3 , 2) and B (6 , 11)

- There is a point divides AB two-thirds from A to B

∵ The coordinates of the endpoints of the directed line segments

   are A = (3 , 2) and B = (6 , 11)

∴ is (3 , 2)

∴ is (6 , 11)

∵ Point (x , y) divides AB two-thirds from A to B

- That means the distance from A to the point (x , y) is 2/3 from

  the distance of the line AB, and the distance from the point (x , y)

  to point B is 1/3 from the distance of the line AB

∴ = 2 : 1

∵

∴ The x-coordinate of the point of division is 5

∵

∴ The y-coordinate of the point of division is 8

∴ The point of division is (5 , 8)

step-by-step explanation:

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