Points j, q, and m are collinear of jm, and jq: qm=2/3
j is located at (2,7), q is located at (5,12), and m is located at (x, y).
what are the values of x and y?

The values of x and y, x = 9.5 , y = 19.5

Step-by-step explanation:

* Lets explain how to solve the problem

∵ Points P , Q and M are collinear

∵ Point Q divides JM where JQ : QM = 2/3

∵ Point J is located at (2 , 7)

∵ Point Q is located at (5 , 12)

∵ Point M is located at (x , y)

- The rule of the point of division is:

  its x-coordinate =

  its y-coordinate =

  where and are the

  endpoints of the segment and , are

  the parts of the ratio

* Lets solve the problem

∵ Q is the point of the division

∵ J is

∵ M is

∵ = 2 and = 3

∴

∴

- Multiply both sides by 5

∴ 25 = 6 + 2x

- Subtract 6 from both sides

∴ 19 = 2x

- Divide both sides by 2

∴ x = 9.5

∴

∴

- Multiply both sides by 5

∴ 60 = 21 + 2y

- Subtract 6 from both sides

∴ 39 = 2y

- Divide both sides by 2

∴ y = 19.5

* The values of x and y are x = 9.5 and y = 19.5

∵ Point M located at (x , y)

∴ Point M located at (9.5 , 19.5)