Answer:
Part A) The straight-line distance between the school and the Fire Station is
Part B) The straight-line distance between the school and the hospital is
Step-by-step explanation:
The full question can be found in the attached image.
Let
The positive x-coordinates represent the East
The positive y-coordinates represent the North
The negative x-coordinates indicate the West
The negative y-coordinates indicate the South
Treat point A (0,0) as the Middle School (reference point).
Part A) The Town Hall is situated 4.3 miles directly east of the Middle School,
thus the coordinates for Town Hall are B(4.3,0).
The Fire Station is positioned 1.7 miles directly north of Town Hall, therefore
the coordinates for the Fire Station are C(4.3,1.7).
What is the straight-line distance between the school and the Fire Station?
Keep in mind that
the distance formula between two points is indicated as
We have
A(0,0) and C(4.3,1.7).
Now substitute
Part B) Now considering
The hospital is 3.1 miles west of the fire station.
The coordinates for the hospital are D(4.3-3.1,1.7).
D(1.2,1.7)
What is the straight-line distance between the school and the hospital?
Remember that
the distance formula applies here as well,
with points A(0,0) and D(1.2,1.7).
Substituting the values gives us
