1.How far is Emilio's house from Diego's house? Explain your answer.
2. Suppose the City Hall is 4 km north of Jose's house, How far is it
from the plaza? from Emilio's house? Explain your answer.
3.How far is the gasoline station from Jose's house if it is 4 km south of
Emilio's house? Explain your answer.
4, What are the coordinates of the points corresponding to the houses of
Jose, Emilio, and Diego? How about the coordinates of the point
corresponding to the plaza?
5.
the City Hall is 4 km north of Jose's house, what are the
coordinates of the point corresponding to it? How about the
coordinates of the point corresponding to the gasoline station if it is
4 km south of Emilio's house?
6. How are you going to use the coordinates of the points in determining
the distance between Emilio's house and the City Hall? Jose's house
and the gasoline station? The distances of the houses of Jose, Emilio,
and Diego from each other? Explain your answer.
Answers
Given : Jose lives 5 km away from Plaza
To Find : 1.How far is Emilio's house from Diego's house?
2 . City Hall is 4 km north of Jose's house, How far is it from the plaza? from Emilio's house?
3.How far is the gasoline station from Jose's house if it is 4 km south of
Emilio's house?
coordinates of the points corresponding to the houses of Jose, Emilio, and Diego and Plaza
Solution:
Coordinates of the points corresponding to the houses and plaza
Emilio's house ( 9 , 4)
Diego's house ( 3 , 12)
Jose's house ( 0 , 0)
Plaza ( 3 , 4)
Emilio's house from Diego's house ( 9 , 4) & ( 3 , 12)
Distance = √(3 - 9)² + ( 12 - 4)² = √(-6)² + 8² = √(36 + 64) = √100 = 10 km
City Hall is 4 km north of Jose's house
Jose's house ( 0 , 0)
=> City Hall = ( 0 , 4)
City Hall from Plaza ( 0 , 4) and ( 3 , 4) = 3 km
City Hall from Emilio's house ( 0 , 4) ( 9 , 4) = 9 km
Gasoline station 4 km south of Emilio's house ( 9 , 4)
=> Gasoline station ( 9 , 0)
Gasoline station from Jose's house ( 9 , 0) and ( 0 , 0) = 9 km
distance between Emilio's house and the City Hall ( 9 , 4) ( 0 , 4) = 9 km
The distances of the houses of Jose, Emilio, and Diego from each other
( 0 , 0) , ( 9 , 4) ( 3 , 12)
Distances = √97 , √153 , 10 km
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