Marissa B.

asked • 04/03/15

Coordinate Question

3. The pirate Dana the Bold has buried her treasure at a distance of 5 paces (1 pace = 1unit on your coordinate system) from a palm tree located at (−3, 4) and √5 paces from a coconut tree located at (−1, −2). Mark all places where the treasure could be buried (find all solutions

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Martin G. answered • 04/03/15

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All the places with a distance of 5 units from the palm tree at (-3,4) form a circle with center (-3,4) and radius 5.
All the places with a distance of √5 units from the palm tree at (-1,-2) form a circle with center (-1,-2) and radius √5.
Draw the circles and see where they intersect.
 
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Marissa B.

Thanks this helps so much! How would I do √5 paces from (-1, -2) circle? Would I do the distance formula and solve for x and y to find potential points on the circle that are √5 paces away from the center? :) 
thanks!
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04/03/15

Marissa B.

Also, I made the circles and idk how to exactly identify what the intersection points are. 
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04/03/15

Martin G.

To solve algebraically, you need the circle equations (=squared distance formula):
circle 1: (x+3)2+(y-4)2=25
circle 2: (x+1)2+(y+2)2=5
Now solve the system of equations.
 
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04/04/15

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