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inessss [21]
3 years ago
7

2. Given a directed line segment with endpoints A(3, 2) and B(6, 11), what is the point that

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
6 0

Answer:

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 (x_{1},y_{1})

 and (x_{2},y_{2}) at ratio m_{1}:m_{2} , then

 x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}} and

 y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}

* 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)

∴ (x_{1},y_{1}) is (3 , 2)

∴ (x_{2},y_{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

∴ m_{1}:m_{2} = 2 : 1

∵ x=\frac{(3)(1)+(6)(2)}{2+1}=\frac{3+12}{3}=\frac{15}{3}=5

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

∵ y=\frac{(2)(1)+(11)(2)}{2+1}=\frac{2+22}{3}=\frac{24}{3}=8

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

∴ The point of division is (5 , 8)

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