1.2+Planning+Emergency+Routes+0910

CS 20th September, 2009 Block F

** 1.2 **

** Big idea: **The dimensions of a right triangle can be determined with limited information.

Essential question: How can I calculate distances on a coordinate grid?

**Euclid****’s chief of police has hired you to map out emergency routes that will allow the paramedics and police officers to arrive at the scene of the accident as quickly as possible. She wants the plan to include routes for automobiles and helicopters.** Pair 1: the police station to City Hall Pair 2: the hospital to City Hall Pair 3: the hospital to the art museum Pair 4: the police station to the stadium
 * The chief of police tell you that your plan must include the shortest routes between the following pairs of locations. Answer parts A and B for each pair of locations. **


 * A. ****1. Give the coordinates of each location, and give precise directions for an emergency car route from the starting location to the ending location.**

Police station- (0, -4) City Hall- (0, 0)
 * 2. ****Find the total distance, in blocks, a police car would have to travel to get from the starting location to the ending location.**
 * A. Pair 1- 1 & 2 **

The car should go north along the X=0 street to reach the City Hall from the police station. The car should travel four blocks north and the City Hall is reached.

The car would have to travel four blocks to get to the City Hall from the police station.


 * Pair 2- 1 & 2**

Hospital- (-6,-4) City Hall- (0, 0)

One possible route (shortest) is that the car should travel north on the X= -6 street until it has reached the Y= 0 street. After reaching this street, the car should turn and travel east on this street. The car should cross 6 blocks and stop at (0, 0). The City Hall is reached.

The car would have to travel 10 blocks to get to the City Hall from the hospital.


 * Pair 3- 1 & 2**

Hospital- (-6,-4) Art museum (6, 1)

One possible route (shortest) is that the car should travel north along the X= -6 street until it has reached the Y= 1 street. After reaching this street, the car should turn and travel east on this street. The car should cross 12 blocks and stop at (6, 1). The art museum is reached.

The car would have to travel 17 blocks in total to get to the art museum from the hospital.


 * Pair 4- 1 & 2**

Police station- (0, -4) Stadium- (-2, 3)

One possible route (shortest) is that the car should travel north along the X= 0 street and crossed 7 blocks till the intersection at (0, 3). It should then turn and travel west along the Y=3 street until it as crossed 2 blocks and reached the intersection at (-2, 3). The stadium is reached.


 * B. ****A helicopter can travel directly from one point to another. Find the total distance, in blocks, a helicopter would have to travel to get from the starting location to the ending location.**

B. For pair 1 the car would have to travel 4 blocks to get to the City Hall from the police station.

For pair 2, the helicopter would have to travel 8 blocks to get to the City Hall from the hospital.

For pair 3, the helicopter would have to travel 13 blocks to get to the art museum from the hospital.

For pair 4, the helicopter would have to travel 8 blocks to get to the stadium from the police station.
 * Problem 1.2 Follow Up **
 * 1. ****How much farther is it from the greenhouse to the stadium by car than by helicopter?**

1. By the car, you need to travel 7 blocks to reach the stadium from the greenhouse. But with a helicopter, you need to travel 6 blocks which is one block less compared to a car.


 * 2. ****How much farther is it from the hospital to the art museum by car than by helicopter?**

2. By the car, you need to travel 17 blocks to reach the art museum from the hospital. But with a helicopter, you need to travel 13 blocks which is four blocks less compared to a car.


 * 3. ****Will the helicopter distance between two locations always be shorter than the car distance? Explain your reasoning.**

3. No, it will not always be shorter by helicopter as there might be cases when the car and the helicopter will have to travel the same distance along the same road (horizontally or vertically).