The planners at the local department at transportation office want to build a highway with two rest stops between the towns. the rest stops will divide the highway into a three equal parts. what are the coordinates of the points at which the rest stop should be build?

The coordinates of the rest stops are (-1 , -1/3) and (1 , 4/3)

Step-by-step explanation:

* Lets explain how to solve the problem

- The rest spots between the two towns will divide the highway

 into three equal parts

- Each part of the highway will be 1/3 the distance between the two

 towns, so the first rest stop will divide the highway at ratio 1 : 2 and

 the second rest stop will be the midway between the first rest stop

 and the second town

- The location of the first town is (-3 , -2) and the location of the

  second town is (3 , 3)

- Assume that the location of the first rest stop is (x , y)

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

 and at ratio , then

  , and

- Let (-3 , -2) is and (3 , 3) is

 and = 1 : 2

∴

∴

∴ The location of the first rest stop is (-1 , -1/3)

∵ The second rest stop is the midway between the first rest stop

   and the second town

∴ The second stop location M is the mid-point between (x , y) and

- The mid-point M is

∴

∴ The location of the second rest stop is (1 , 4/3)

* The coordinates of the rest stops are (-1 , -1/3) and (1 , 4/3)

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y