a.
To find how many points are there on Earth’s surface that are equidistant from Houston and Toronto.
a.
Answer to Problem 23WE
Infinitely many points
Explanation of Solution
Given:
Earth
Assume that the Earth is a sphere.
For this case let us consider two points
The points that are equidistant from both these cities would simply be the line segment between these two points
For a sphere two points can be equidistant from an infinitely many number of points.
Conclusion:
Therefore, there are infinitely many number of points that are equidistant from Houston and Toronto.
b.
To find how many points are there on Earth’s surface that are equidistant from Houston, Toronto and Los Angeles.
b.
Answer to Problem 23WE
Two points
Explanation of Solution
Given:
Earth
Assume that the Earth is a sphere.
For this case there are two points
There will only be two points that will be equidistant from all the three cities.
Conclusion:
Therefore, there are two points that are equidistant from Houston, Toronto and Los Angeles.
c.
To find how many points are there on Earth’s surface that are equidistant from Houston, Toronto, Los Angeles, and Mexico City.
c.
Answer to Problem 23WE
No point
Explanation of Solution
Given:
Earth
Assume that the Earth is a sphere.
For this case there are two points
There will be no point that will be equidistant from the 4 points.
Conclusion:
Therefore, there will be no point that will be equidistant from Houston, Toronto, Los Angeles and Mexico City.
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