A, b and c are collinear and b is between a and c. the ratio of ab to ac is 3: 2. if a is at (4,8) and b is at (7,2) what are the coordinates of point c

The coordinates of point C are (9 , -2)

Step-by-step explanation:

* Lets explain how to solve the problem

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

  and at ratio

 from the first point , then

  and

* Lets solve the problem

- A, B and C are collinear and B is between A and C

∴ Point A is

∴ Point C is

∴ Point B is (x , y)

- The ratio of AB to BC is 3 : 2

∴ = 3 : 2

* Lets use the rule above to find the coordinates of point C

∵ A = (4 , 8) and B = (7 , 2)

∵ = 3 : 2

∴  

- Multiply each side by 5

∴  

- Subtract 8 from both sides

∴

- Divide both sides by 3

∴

∴ The x-coordinate of point C is 9

∴  

- Multiply each side by 5

∴  

- Subtract 16 from both sides

∴

- Divide both sides by 3

∴

∴ The y-coordinate of point C is -2

* The coordinates of point C are (9 , -2)

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step-by-step explanation: there is no picture