A, b,and c are collinear, and b is between a and c. the ratio of ab to ac is 2: 7.
if a is at (0,-8) and b is at (2,-4), what are the coordinates of point c?
c=( , )

The coordinates of point C are (7 , 6)

Step-by-step explanation:

* Lets explain how to solve the problem

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

  and at ratio

 from the first point, then

 and

* Lets use this rule to solve the problem

- A, B, and C are col-linear, and B is between A and C

∴ A is

∴ C is

∴ B is (x , y)

- The ratio of AB to AC is 2 : 7

∵ AB : AC = 2 : 7

∴ AB is 2 parts of AC and BC is (7 - 2) = 5 parts of AC

∴ AB : BC = 2 : 5

∴

∵ A = (0 , -8)

∴ = (0 , -8)

∵ B = (2 , -4)

∴ (x , y) = (2 , -4)

∵

∴

∴

- Multiply both sides by 7

∴

- Divide both sides by 2

∴

* The x-coordinate of point C is 7

∵

∴

- Multiply both sides by 7

∴

- Add 40 to both sides

∴

- Divide both sides by 2

∴

* The y-coordinate of point C is 6

∴ The coordinates of point C are (7 , 6)

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step-by-step explanation:

answer: y=4000x+14000

step-by-step explanation: