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Question 1167217: kelly and her friends agreed to share internet connection with one another. they placed the router at the center of their dorm. the router has a range of 15 meters. joana’s room is located 5 meters east and 5 meters north of the router. cherry’s room is located 10 meters east and 15 meters south of the router. kelly’s room is located 5 meters west, and 10 meters north of the router, and bella’s room is located 10 meters south of the router. who among them has no access to the internet connection?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! joana is 5 meters east and 5 meters north.
this forms a right triangle.
the hypotenuse of this right triangle is equal to sqrt(5^2 + 5^2) = sqrt(50) = 7.07 meters from the router.
no problem there - she is in range.
cherry is 10 meters east and 15 meters south..
already there's a potential problem because the hypotenuse will be larger than 15 meters away.
specifically, her distance from the route is sqrt(10^2 + 15^2) = sqrt(100 + 225_) = sqrt(325) = 18.027 meters from the router.
she is out of range. !!!!!
kelly is 5 meters north and 10 meters south.
the hypotenuse of her right triangle is sqrt(5^2 + 10^2) = sqrt(150) = 12.247 meters away from the meter.
no problem there - she is in range.
bella is 10 meters south.
no problem there - she's in range.
this is what the problem looks like on a graph.
on the graph, .....
joana is at (5,5)
cherry is at (10,-15)
kelly is at (-5,10)
bella is at (0,-10)
it's easy to see just by looking at the graph that cherry is out or range.
the coordinates are in (x,y) format.
x is the number of units from the point (0,0) in a horizontal direction.
y is the number of units from the point (0,0) in a vertical direction.
the point (0,0) is the center of the graph and is called the origin.
for example:
the point (-5,10) would be 5 units horizontally to the left of the origin and 10 units above the origin.
west is left of the origin.
north is above the origin.
east is right of the origin.
south is below the origin.
the point (0,0) and the point (-5,10) form a right triangle.
5 units to the left of the origin is the horizontal side of the triangle.
10 units north of the origin is the vertical side of the triangle.
the direct distance from the origin to the point (-5,10) is the hypotenuse of the right triangle.
on the graph, you can draw the lines and it will look like this.
that's 5 meters going west and 10 meters going north.
the direct line distance is the hypotenuse of the right triangle, whose length is equal to sqrt(5^2 + 10^2).
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